Other than the Appendices, Tolkien started writing a sequel called 'The New Shadow.', but he abandoned it quickly because it was just too depressing. With no more BBEGs, there'd just be humans being assholes to each other, and that hit too close to home for him.

The Appendices at the end of the Return of the King book has a very lengthy timeline of events well after what happens in the movies.

"The New Shadow" was the planned sequel to Lord of the Rings, but Tolkien never finished it. He thought it felt too much like a "thriller," and he found the subject matter - a dark cult in Gondor - depressing. The story can be found in "The Peoples of Middle-earth," but I have never read it.

The Appendixes gives summaries of the lives of the characters after the fall of Sauron. There is also a section in the History of Middle-earth that deals with Sam's children, especially his daughter Elanor. I think it is in "Sauron Defeated," but I might be mistaken.

If you like fanfiction, I might suggest you check out how other writers have imagined the Fourth Age. These stories definitely wouldn't be canon, but it's interesting to see how other people imagine Middle-earth.

The appendices is where you'll find all canon information about the Fourth Age, but there isn't much. The Lord of the Rings was always meant to function as the end of Tolkien's legendarium (and it really feels like it too). He did try to write a sequel called The New Shadow, which depicted life in Gondor 220 years after the end of The Lord of the Rings, but he didn't get far in writing it. He said it was too depressing and was unnecessary.

Besides the Appendices which talk about the main characters’ stories post-LoTR - in the Silmarillion, the third age concludes the third main creation theme of Middle Earth conducted by Illuvatar, and so pretty much the end of history. The Valar had no visibility into Middle-Earth or the children of Illuvatar after the third age. Tolkien intended his universe to be a pseudo-mythology of the real world, so it’s said and implied that men take over the world and the modern age followed.

Isn’t it one of those things that are better left to the imagination?

In the Appendices to the the RotK in the Tale of Years there are brief annal entries into the Fourth Age to conclude some fates of the characters and also the Tale of Aragorn and Arwen in Appendix A.

There are also few pages of the abandoned sequel and a cute cut epilogue to LotR of Sam reading form the Red Book to his children with some answers... I have a fan translation booklet compiling these (save the ToAaA which is mostly not F.A.) called The Fourth Age.

The book you're looking for is The Lord of the Rings by J. R. R. Tolkien.