Liberation of Kashyyyk
Despite the fall of the Emperor at Endor, some Imperial sectors blocked news of his death from being released so the local Imperial Moffs could retain their control in the interim. This was the case at Kashyyyk, the home of the Wookiees, who had been enslaved by the Empire since shortly after the end of the Clone Wars. While Chewbacca had a sworn life debt to Han Solo for liberating him years earlier, Han had also repeatedly promised to return to Kashyyyk to free the rest of his people (including his family) one day.
When word came across that the time was right, Han abandoned his post as a General in the New Republic to go free the Wookiees. Unfortunately, his intel was bad and Chewbacca got captured and Han had to flee, leaving his friend behind. After teaming up with a crack team from the New Republic, he's able to return and free Chewbacca and many other Wookiees, starting a rebellion on the ground, while New Republic forces led by Wedge Antilles and Admiral Ackbar eventually arrive to secure space above the planet, making the Wookiees free beings for the first time in decades.
Battle of Jakku and Imperial Retreat
Eventually, the Empire withdraws virtually all its remaining forces to the remote planet of Jakku, which, as only a few high ranking Imperials know, is the final stage of Palpatine's Contingency. After decades of mining under the supervision of Gallius Rax, the Imperial outpost had drilled a shaft all the way to the planet's core, enabling Palpatine to basically turn Jakku into a ticking time bomb.
The Imperial forces fought with an undisciplined ferocity the New Republic wasn't familiar with, making the battle exceptionally tough, but eventually, they succeeded in turning the tide, despite a number of Star Destroyers engaging in suicide missions to crash into the planet's surface while pulling New Republic ships in their tractor beams. Palpatine's plan to explode the planet was supposed to eliminate all forces, both Imperial and New Republic, anywhere near the planet, but the contingency was foiled at the last moment, saving the planet as the New Republic defeated the remaining forces.
Still, an Imperial shuttle departed shortly before the planet was expected to explode, bearing Grand Admiral Rae Sloane, Stormtrooper instructor extraordinaire Brendol Hux, his son Armitage Hux, and a number of young slaves from Jakku who were already being conditioned as the next generation of Imperial soldiers. Following the path charted into the Unknown Regions, the shuttle met up with Emperor Palpatine's personal Super Star Destroyer, the Eclipse, which had fled the galaxy before the Battle of Endor under the command of unknown officers and crew.
A New Jedi Order
With the Empire seemingly gone and the fledgling New Republic finding its footing, Luke Skywalker, the hero of the Rebellion, is now free to dedicate himself to restoring the Jedi order. He had already begun scouting out many of Palpatine's old research outposts, recovering saplings of a Force-sensitive tree from the courtyard of the Jedi Temple on Coruscant (with possible ties back to a much older Jedi temple), a special compass hidden away by the Emperor, and possibly more. He also works closely with Lor San Tekka and the Church of the Force, who had worked in secret during the reign of the Empire to preserve the legacy of the Jedi.
Luke doesn't merely seek out former Jedi teaching, but some legends also have him visiting a number of different cultures to learn different aspects of the Force for a more holistic perspective rather than simply picking up where the old Jedi Order left off.