During the Lord of the Rings films, a lot of world-altering events took place. Several evil regimes were overthrown, elves left the world for good, and Merry and Pippin introduced whole new kinds of smokeable herbs to The Shire.
A TV show that explored the pre-existing characters learning to fit in to this new world would be a very interesting way to explore the future of the land, and would give fans a chance to return to several beloved characters. Several actors, like Ian McKellen (Gandalf) and Sean Astin (Sam Gamgee) have already expressed interest in returning, so you know they're up for it. Although the ending of the final film nullifies some of those options...
Even if not all the characters returned, it could be interesting to follow people from the surviving factions and see how they understand the world. What about an expedition into the ruined Mordor, or a Kylo Ren -style imitator trying to emulate an evil overlord, who must be overthrown?
The death of Sauron likely wouldn't remove all evil from the world - in the book it certainly didn't. Any number of lurking evils still exist in the world, and a plot to remove one of these would make for an exciting show. Perhaps we could see a return to the mines of Moria to drive out the goblins, or an adventure to the south of Middle-Earth to recruit the Haradrim to the forces of good.
This would give the showrunner a lot of creative freedom, although if they needed help Tolkien's Silmarillion included snippets of information on the fate of beloved characters.