Galadriel's role in The Lord of the Rings, either in the book or in Peter Jackson's film trilogy, is brief but has a serious impact on the story.
Her insight, inspiration, and gifts help and encourage numerous characters to the very end, and her actions, both on and off screen, helped bring about Sauron's defeat.
But after Sauron is gone and all is said and done, Galadriel is only shown leaving Middle-earth with Gandalf and Elrond.
So what exactly happened to her when the war was over?
Well, while The Lord of the Rings: The Rings of Power is by no means faithful to Tolkien's canon, it does get one thing right about Galadriel's character – she had fought relentlessly against Sauron throughout two ages of Middle-earth, for several thousand years. And when the Dark Lord finally fell, she had certainly earned a much-needed rest.
After Sauron's fall, she led her forces in one last battle, helping the wood elves under King Thranduil to attack the fortress of Dol Guldur in the Mirkwood forest, which had been Sauron's refuge for many centuries.
Though orcs, trolls, and other servile creatures were thrown into madness and chaos by the loss of their master, human followers of Sauron apparently still fought here and there.
With her power, Galadriel helped to raze Dol Guldur to the ground. And this was the last battle she ever fought.
Weary from the millennia-long struggle, and without her ring of power to halt the passage of time and preserve her strength indefinitely, she decided to leave Middle-earth for good. She spent only a few months there. In the book, she attended Aragorn's wedding and coronation, which marked the beginning of peace in the land, and had some meetings with Gandalf and others as she traveled from Gondor to the Grey Havens.
Finally, Galadriel said her last farewells and sailed back to the Undying Lands on a boat with elves and Ring-bearers. What happened to her after that is never mentioned, but presumably she reunited with her old friends and relatives and lived happily until the end of time.