This image is to help explain the state of affairs for my Star Wars Fanfiction Series: Star Wars: The Shadow Wars. The series is currently between "Seasons."
Note: The information below is from my own universe which is a blend of old and new canon and it not to be considered canon in any other universe but mine.
This image was acquired through Star Wars: Empire at War
Formal Name: The Galactic Republic
Informal Name(s): The New Republic, The Republic
Head of State: Supreme Chancellor - Leia Organa-Solo (Incumbent), originally Chief of State
Government: Democratic Republic
Date Established: 2 BBY (as the Alliance to Restore the Republic/Rebel Alliance), 4 ABY (informally as the New Republic), 5 ABY (formally as New Republic)
Founding Document: Declaration of a New Republic
Constitution: New Republic Common Charter
Head of Government: Supreme Chancellor (9 ABY-present), Chief of State (4 ABY - 9 ABY)
Commander-in-Chief: Supreme Commander (informally known as Grand General) - Supreme Commander Galen "Starkiller" Marek
Executive Branch: Republic Cabinet (Formerly Alliance Cabinet)
Legislative Branch: Galactic Senate
Judicial Branch: Courts of Justice
Capital: Republic City - Coruscant
Motto: "In the Force we Trust"
State Religious Body: The New Jedi Order (Unofficially), Agnostic (Legally)
Official language: Galactic Basic
Currency: Republic Dataries (i.e. Republic Credits)
Anthem: The Star Wars by Nohj Billiams (A/N: The classic Star Wars theme by John Williams)
Insignia: The New Republic Starbird (Blue variant of the Marek Family Crest)
Formed from: The Alliance to Restore the Republic/The Rebel Alliance
"Today, we stand before the Galaxy to celebrate a Return! A Return to Democracy! A Return to Freedom! A Return to Liberty! Let it be recognized by all those alive today and millennia from now, that despite the best efforts of tyrants and dictators, liberty and freedom are valued most by the people, more than tyranny and oppression! May the Force be forever with this, the New Republic!" - Mon Mothma during her inaugural address as the first elected Chief of State of the New Republic in 5 ABY.
The New Republic, the long intended and hard fought goal of the Rebel Alliance, was born out of what was once a fledgling group of freedom fighers who opposed the formation of the Galactic Empire from the ashes of the Old Republic. The Rebel Alliance started as a large collection of scattered and largely independant cells of Rebels operating throughout the galaxy, working to slow or reverse the Empire's gradual expansion and increasing grip on the galaxy. These cells are known to have been in operation as early as 19 BBY, the day the Empire was founded. Bail Organa, the Senator from Alderaan, is largely considered to have been the "First Rebel" in his covert assisting of Jedi Masters Obi-Wan Kenobi and Grand Master Yoda go into hiding as well as helping numerous Jedi go into hiding while also laying the ground work for additional Rebel cells to be formed. It wasn't until 2 BBY, with the Corellian Treaty, that the Rebel Alliance formally came into existance and the Galactic Civil War truly began. The Rebellion wouldn't claim their first major victory until the Battle of Atollion in 2 BBY which saw a major tactical victory against the Empire's Grand Admiral Thrawn by Galen Marek who took the place of Jedi General Rahm Kota as the military leader of the Rebellion. In Year Zero, the Rebellion successfully carried out the Battle of Yavin which saw the destruction of the Empire's terrible superweapon, the Death Star, which showed the galaxy that the Empire could be beaten. Afterwards the Galactic Civil War ramped up as millions flocked to the Rebellion to avenge the Empire's destruction of Alderaan with the Death Star. The Rebellion suffered serious setbacks such as the loss of Echo Base during the Battle of Hoth in 3 ABY but ultimately achieved victory over the Empire with Emperor Palpatine during the Battle of Endor in 4 ABY, the Liberation of Coruscant and the Battle of Jakku in 5 ABY which saw the strategic defeat of the Empire which would be officially declared defunct following the Battle of Bastion in 11 ABY.
The transition from Galactic Empire to the New Republic started slowly at first, beginning almost instantly after the Battle of Endor. The New Republic would adopt much of the same governmental structuring as the Old Republic but with several noticable modifications and the addition of several checks and balances to make sure another Palpatine could not usurp control of the government. The Alliance Cabinet, the leading figures of the Alliance itself, all agreed that Mon Mothma was to be the interum Chief of State until the first elections could be held (although this decision was made in Year Zero in the wake of Yavin). After the Liberation of Coruscant and the Battle of Jakku, Mothma was nominated by Leia Organa for the first elections for Chief of State. Mothma's opponents included Senator Garm Bel Iblis, General Lando Calrissian, and two other politicians but Mothma won a decisive majority and even most of her opponents, with the possible exception of Bel Iblis, considered themselves just "opponents in name only" and were in general agreement that Mothma was the best choice. It was originally hoped that Jedi Knight, Galen Marek, the Jedi that many considered to be the Founder of the Rebellion and the one who led them to victory over the Empire, would run for Chief of State but Galen declined, wishing to take his newlywed wife, Juno Eclipse, into the galaxy to live in peace after nearly 8 long years of war. He did give his endorsements of Mothma and Admiral Gial Ackbar for the posts of Chief of State and Supreme Commander, respectively.
Since 5 ABY, the New Republic has had to contend with the Imperial Remnant, the remains of the Empire that continued to resist the Republic's rise to power. Over time, the Remnant dwindled away due to infighting between ex-Moffs turned Warlords and from the Republic's own efforts. Admiral Thrawn briefly appeared with his Empire of the Hand and came closest to defeating the New Republic but he too failed and was presumed killed at the Battle of Bilbringi. Emperor Palpatine reappeared in 10 ABY and led a revived Empire but he was finally defeated for good in 11 ABY by his former Apprentice, Anakin Skywalker, on Coruscant. Palpatine's death led to the Imperial Remnant consolidating their power in the systems surrounding Bastion but again, infighting amongst the surviving Imperials only aided the Republic in defeating the Empire for good in 11 ABY at the Battle of Bastion.
One of the incidents that some believe helped to weaken the crumbling Empire's power was easily the most controversial bill passed by the New Republic Senate. This bill, commonly known as the Forgiveness Act, granted amnesty and immunity to any and all Imperial Officers below the rank of Sector Moff who surrendered themselves to the Republic before the tenth anniversary of the Battle of Yavin (10 ABY). This included most if not all of the Imperials that had already joined the Rebellion by that time. Anakin Skywalker's former persona of Darth Vader was also included for his having helped turn the tide at the Battle of Endor by stepping aside and allowing Galen Marek to defeat the Emperor and again for helping turn the tide at Jakku by executing Director Ysanne Issard and ordering the execution of Imperial Warlord Zsinj during the same battle before ordering the remaining Imperial forces to stand down and surrender. The only condition to this immunity deal is that the Imperials who surrender confess in full to any actions they had taken as part of the Empire. Moffs however were tried for high crimes against the Republic and for countless sapient rights violations. All of the Moffs tried were proven fanatics of the Empire and demonstrated their loyalty to the Empire during their trials. The Moffs' individual fates were ultimately decided by the very systems they lorded over for the Empire with most being executed for their crimes. Only two Moffs escaped execution and were sentenced to life imprisonment where they have remained. One died of natural causes while the other was assassinated in his cell by a prison guard who was a citizen from that Moff's sector. Regardless, the effect this bill had was incredible as countless Imperials lined up to surrender, one instance seeing an entire fleet of Imperial Warships arriving to surrender to the Republic.
The New Republic quickly formed the Republic Senate, reforming it after the Empire had dissolved the senate in Year Zero. The Senate functions much like the Senate of old did but with a few notable differences. The Senate no longer allows large corporations like the Trade Federation or the Banking Clan to have Senate Seats. They are allowed to have representatives which are effectively senators without the power to cast a vote. They can propose legislation but beyond that they cannot do much else except for voice support/objection to certain subjects but this is but one example. For the first four years of the Republic, the Chief of State was the modern parallel to the Supreme Chancellorship of the Old Republic. It was intended to try and get away from reminding the galaxy of how Palpatine rose to power, believing the Chancellorship had been sullied beyond repair but most senators and diplomats kept referring to or addressing Mon Mothma as Chancellor until finally Senator Iblis proposed they simply alter the formal title from Chief of State to Supreme Chancellor. Most in the Republic preferred the title of Chancellor, feeling it had more weight to it than Chief of State. Finally after relatively little debate, in 9 ABY, the Chief of State title was changed to Supreme Chancellor by a majority vote in the Senate. This vote was mildly ridiculed as it was so trivial a subject that still warranted a vote. There was no addition or removal of any powers with this vote, just a formal name change.
The Republic grew rather quickly as most systems quickly accepted, especially after Jakku, that the Empire was dead or dying and the Imperial Remnant simply wasn't enough to warrant continued loyalties. Many systems were economically coerced into joining the Republic as most of the member systems were enjoying improved trade with the relaxed trade restrictions the New Republic put in place. The Republic was noticeably less controlling than the Empire as there weren't Imperial Stormtroopers stopping and searching anyone who seemed suspicious. Certain inhumane practices such as slavery was heavily cracked down on. The Republic's staunch anti-slavery stance, referred to as the Shmi Policy (named after Shmi Skywalker, the mother of Anakin Skywalker), has resulted in a small handful of systems such as Trandosha and Zygerria outright refusing to join the Republic, these systems remaining apart and unaffiliated since the Republic's formation. The Hutts are a unique matter as while their systems are not considered member states of the Republic, they do grant the Republic some level of authority and jurisdiction within their space so long as it doesn't cut into their own affairs. Most systems are allowed to function autonomously and a lot of leeway is given to sector rights on most issues with some exceptions (slavery, extradition rights, illicit goods, etc.).
The appointment of senators is also a matter left to each system to determine. For instance, Naboo's senator is appointed by the reigning King or Queen and serves at their pleasure. Lothal however determines their senator by democratic popular vote, with candidates vetted via a primary system in each party with the victors moving on to face their opponents in the main election. The only time all systems conform to a single voting method is for Chancellery elections. When it comes time for the election of a new Chancellor, every citizen in the Republic casts a vote with their registered homeworld, each system being allotted one vote each. When the vote is tallied on a system, the candidate with the most votes receives that system's vote, the Senator of that system being bound by law to submit their vote for the winning candidate at the following Senate Meeting. Once all systems have voted or when it is clear that one candidate has, mathematically, secured enough system votes to win the Chancellorship, the vote is then moved to the Senate where the votes are formally cast on behalf of the systems. Galactic Popular Vote is not considered as a deciding metric due to the sometimes massive differences in populations between systems. Ergo, only the system's vote is decided by popular vote. This was the electoral process used during the first Chancellery election and has continued ever since with Mon Mothma serving as the first Chief of State/Chancellor from 5 ABY to 20 ABY when she formally retired. Leia Organa-Solo was then elected to the Chancellorship that same year, winning reelection in 25 ABY to a second term and is the present incumbent Chancellor. Leia initially had been floating ideas of not seeking a third term but with the outbreak of the Shadow Wars in 28 ABY, the senate has been discussing the triggering of Article 11, Paragraph 38 of the Republic Constitution which allows the Senate to vote to extend the Chancellor's term in a time of war.
On currency, the Republic has continued the single unifying currency established by the Empire only using Republic Dataries (Credits) instead of Imperial. Nova Crystals and Aurodium as well as other raw materials are also accepted. Old Imperial Dataries are still accepted but have gradually disappeared, with some people keeping Imperial Credit notes for collectors items. Some businesses, especially ones established during the Empire (or prior to) keep a framed Imperial Credit note for the sake of how long they've been in business, sometimes even with an Old Republic and/or even Separatist credit note on display to demonstrate the business's age.
The Jedi Order has returned to a position of religious authority within the Republic, having a similar position that they did immediately prior to the Clone Wars. Although the Jedi have a noticeable influence on the Republic, they aren't considered the official state religion, at least on paper, as most systems have their own religious systems that are still in practice. These religions have received some level of recognition from the Republic provided certain conditions of non-violence are met. These conditions usually refer to religious institutions that preach non-believers be killed or individuals who leave must suffer some kind of injury to mark them as heretics. Other examples of these conditions include the more infamous case of the Zealots of Psusan who were discovered to have been using illegal mind altering drugs to brainwash their all-female members into becoming High Priest Scri Oscuro's private harem. Oscuro's journal revealed the cult to be nothing more than a grand scheme to achieve such a goal that he'd been successful in carrying out for almost 30 years. Oscuro was torn to shreds by his enraged congregation when the truth was revealed. Republic religious liberties laws were quickly adapted to include the banning of already illegal brainwashing techniques.
The Anthem of the New Republic is "The Star Wars" by Nohj Billiams. Billiams is most well known for having written the Imperial March not long after the formation of the Galactic Empire, but after the Battle of Yavin, he defected to the Rebellion, joining their efforts as a propaganda specialist. The reason for his defection was self-explanatory: His homeworld had been Alderaan. "The Star Wars" was composed to celebrate the Rebellion's victory at Endor and was adopted as the Republic's National Anthem in 7 ABY. Yub Nub, a song sung by the Ewoks after Endor had been considered but was passed on by the Senate as the Ewoks didn't have any representation within the Republic short of being a protected system.
Citizens of the Republic enjoy a lot more freedoms than they did during the Empire, such as the right to bear and keep arms, voting rights, in certain cases droids can be granted independence and citizenship, and the Republic regularly enforces anti-trust laws to make sure monopolies don't occur so as to keep the market competitive. Trade is also very much open between systems, regardless of if they're member states of the Republic or not. It's only been since the outbreak of the Shadow Wars that certain systems are declared out of bounds to trade, these systems usually being Sith controlled systems. Neutral systems are still eligible for trade with minimal trade tariffs in place. The holonet is also free and open to the Republic's citizens now as opposed to the Empire's strict control over it. The Empire had restricted the holonet to Imperial military use but the Republic has returned public access to the service.
The Republic's insignia is the Republic Starbird which is a blue variation of the Marek Family crest set against a black circle within a ring of 15 white stars and an outer ring of gold. The usage of the crest was a subject of debate for the Republic as continuing to use the insignia seemed like swearing fealty to the Marek family to some. Marek also would have to sign off on its continued usage. A compromise was eventually reached where the Republic would appropriate the family crest only in a blue variation with the aforementioned decorations while the Marek family itself would continue using the classic red variation without any additional decoration.
Militarily, the Republic uses an all volunteer military. All prospective soldiers are trained at various training centers across the galaxy. The Republic Military uses mostly leftover ships from the Rebellion as well as ships acquired from surrendering Imperials but have been slowly phasing out these older vessels. It's still not uncommon though to see ships dating back as far as the Clone Wars being used in front-line operations by the Republic. The Mon Calamari Shipyards, Corellian Engineering Corporation, Kuat Drive Yards, and the Republic Engineering Corporation (a privately owned company) manufactures the bulk of the Republic's fleets while Incom-Freitek, Slayn & Korpil, and Koensayr Manufacturing produce the bulk of the Republic's starfighter forces. Baktoid Armor Workshop, Yutrane-Trackata, Rothana Heavy Engineering, Aratech Corporation, and Loratus Manufacturing produce the Republic's ground vehicles. The Mandalorian owned MandalMotors and Mandal Hypernautics have recently, as of 28 ABY, entered competition with the Republic's other arms manufacturers to produce the Republic's war machines. Although there has been talk of adopting a more uniform look to their fleets like the Old Republic and Galactic Empire did with their ships (i.e. predominant design traits such as the arrow shaped Star Destroyers), the New Republic Military has opted instead to keep a diverse array of ship designs as a symbol of how each race within the New Republic is united under a single banner but ultimately individual. This is part of a policy known as the "One for the many, many for the one" policy. This gives New Republic Military Contractors more freedom and leeway to develop new ships without having to try and conform to a single design scheme and the military itself tends to prefer ships (and personnel) based on merit, not aesthetics. "If it works, it works." is a phrase that gets mentioned every so often.
The Military is led by the Supreme Commander who answers to the Chancellor and the Senate. The first Supreme Commander was Gial Ackbar who served for almost twenty years before retiring, his niece, Jesmin Ackbar, taking the position of Supreme Commander until 28 ABY when she abdicated the position to Galen Marek at the outbreak of the Shadow Wars. Marek's return as Supreme Commander was heralded with Holonet Headlines of "THE STARKILLER IS BACK!!!"
In terms of territory, the Republic controls most of the "Old Territory," a colloquialism for the territory once controlled by the Old Republic during the height of its power, with only a few systems, mostly in the outer rim, refusing to join the Republic. With the outbreak of the Shadow Wars, hundreds of systems have either left the Republic voluntarily to join the Sith, declare neutrality or have been conquered by the Sith Empire, leaving their long term political allegiances in question. The Republic still controls a majority of the galaxy but the Sith, especially after Operation: Blind Side saw the Sith gain considerable ground, have made significant gains.
It's interesting to note that the Sith and any former Imperials that might serve them, still refer to Republic loyalists as "Rebels." The phrase "Rebel scum" still being prevalent, although the more modern "Republic scum" is still common.
What probably didn't go over well with some companies was that some companies had a monopoly with the Empire such as Sienar Fleet Systems who built the TIE Fighers, Kuat Drive Yards who built the Star Destroyers, and Rothana Heavy Engineering who built the bulk of the Empire's walkers. Those three might not have liked it now the other companies could compete with them for contracts with the Republic. Those companies may or may not have military contracts with the Republic but they still stand a good chance provided they build something the Republic need. I also think it's safe to say that with the Shadow Wars, these companies will have plenty of business.
It reminds me of Star Trek's Ferengi Rules of Acquisition: Rule 34 - "War is good for business" and if your business is war machines, you've got yourself a golden opportunity.