George Lucas sketched out several drafts of the franchise’s future trilogy, which would continue the story of Luke, Leia, and the New Republic, prior to the sale of Star Wars to Disney. He spoke about one of them in the book The Star Wars Archives: Episodes I-III, which is preparing for release.
In it, Darth Maul was supposed to return to the universe, who took Darth Talon, the Sith Lord from the expanded universe, for training. In it, she was the storm of the Jedi in 137 after the Battle of Yavin. George wanted to change her fate and write her into history earlier.
Maul himself was supposed to act as Darth Sidious of the new trilogy, and Talon was supposed to be a kind of analogue of Darth Vader. The legless Sith established dominion over the galaxy through a criminal network of shadows, undermining the work of the New Republic.
In the trilogy, Leia would work to rebuild the Republic and become the new Supreme Chancellor, while Luke would work to rebuild the Jedi Order with Order 66 survivors and children with Force potential. Both Skywalkers face new Sith.
The story should have had an interesting twist in that Leia, not Anakin, would bring real balance to power. Towards the end, the Order is revived and the New Republic flourishes under Leia’s rule.
It is possible that some of these plot elements can still be adapted into a plot set between the events of the original trilogy and the sequel trilogy. All we know is that Luke was trying to create a new Order and Leia was helping the New Republic.