Following the victory at the Battle of Endor the Rebel Alliance formed a new government called the New Republic. Just over a year after the Battle of Endor the New Republic engaged Imperial forces on the far off world of Jakku, defeating the Imperial fleet there and leaving the remains of a number of startships scattered over the planet.
After the Battle of Jakku the New Republic forced the Galactic Empire to sign the Galactic Concordance, which brought an end to the war between the two states. The Imperials were forced to give a number of concessions, including the outlawing of torture, ceding Coruscant to the New Republic, and remaining within strictly defined treaty boundaries.
Following the signing of the Concordance many Imperial warships than began making hyperspace jumps in to the Unknown Regions of the galaxy. Away from the scrutiny of the New Republic these Imperials formed a military junta called the First Order.
Becoming complacent in the apparent peace that followed, the New Republic reduced its military footprint considerably. The First Order took advantage of the New Republic's complacency and began rearming in violation of the treaty.
Meanwhile the New Republic was paralysed by political strife between Centrists who wanted the New Republic to have a strong centralized government, and the Populists who favored a decentralized Democracy. Leia Organa was a leading populist until it was revealed she was the daughter of Darth Vader. This destroyed her political career and she left the Senate not long afterwrds.
Seeing that the New Republic was unwilling to do anything about the First Order, Leia helped form the Resistance to oppose the First Order. Many of her old Alliance comrades such as Admiral Ackbar joined her, along with a number of others.
The New Republic suffered a critical blow when their capital planet of Hosnian Prime was destroyed by the First Order's Starkiller. This wiped out the Senate and a large part of the New Republic Starfleet. However, before the Starkiller could destroy any more planets a Resistance strike team destroyed the Imperial superweapon.
As in the canon continuity the Rebel Alliance organized itself into the New Republic following the Battle of Endor. Two years after the Battle of Endor the New Republic retook Coruscant. The first Chief of State was Mon Mothma, and she was followed by Princess Leia after Mothma stepped down due to her health being badly affected by Ambassador Furgan's nano destroyers.
For most of its existence the New Republic fought various Imperial holdouts, such as Grand Admiral Thrawn and other Imperial warlords. Emperor Palpatine returned from the dead about six years after Endor in a clone body. He briefly succeeded in turning Luke Skywalker to the dark side of the force and nearly toppled the New Republic before his last clone was destroyed and he was consigned to chaos for all eternity.
The following year Admiral Natasi Daala emerged from the Maw Installation, and succeeded in reuniting the various Imperial factions into a main remnant. After she left command Gilad Pellaeon took over command, and continued to fight the New Republic. Despite the new unity amongst the Imperials, the remnant continued to lose power and influence until it consisted of eight systems in the galactic backwater.
In 19 ABY Pellaeon came to the conclusion that it was useless to continue hostilities against the New Republic, that if they kept fighting the Empire would be destroyed but if they stopped some Imperial ideals might survive. Despite the attempts of Imperial hardliners to derail the peace process, Pellaeon was able to successfully negotiate a deal with the New Republic. After two decades the Galactic Civil War was finally over.
The peace would not last long. A few years later the extra galactic Yuuzan Vong invaded the galaxy in what would come to be known as the Yuuzan Vong War. The New Republic was caught completely flat footed by the invasion by beings who were apparently outside the Force. Over the next few years the New Republic suffered a series of defeats culminating in the conquest of Coruscant by the Vong. After the New Republic was forced to abandon Coruscant, the New Republic was reorganized into the Galactic Federation of Free Alliances.