At the end of the book series, hobbits and elves sail to the east of the middle earth to unknown places and only humans stay in the Middle Earth. What happened next? Where did elves settled down? Were there any other adventures? Will there be a sequel to LOTR series?
Tolkien begun, but didn't complete, a sequel called the New Shadow which eventually saw publication in History of Middle-earth 12.
In his own words (Letter 256):
I did begin a story placed about 100 years after the Downfall [of Mordor], but it proved both sinister and depressing. Since we are dealing with Men it is inevitable that we should be concerned with the most regrettable feature of their nature: their quick satiety with good. So that the people of Gondor in times of peace, justice and prosperity, would become discontented and restless – while the dynasts descended from Aragorn would become just kings and governors – like Denethor or worse. I found that even so early there was an outcrop of revolutionary plots, about a centre of secret Satanistic religion; while Gondorian boys were playing at being Orcs and going round doing damage. I could have written a 'thriller' about the plot and its discovery and overthrow – but it would be just that. Not worth doing.
Not as a sequence per se, but as an apocalypse of sorts; the Dagor Dagorath or Last Battle and Day of Doom.
Quoting the Second Profecy of Mandos:
[...] When the world is old and the Powers grow weary, then Morgoth, seeing that the guard sleepeth, shall come back through the Door of the Night out of the Timeless Void; and he shall destroy the Sun and the Moon.
(Truly) epic battle ensues.
"Will there be a sequel" -- not officially unless someone convinces the Tolkien estate that they can produce something which is completely true to JRRT's ideas and ideals and language. Odds of that happening are close to nil.
I'm sure there's lots of fan-fiction out there. Not canon, of course.
I don't know if anyone has established whether any of Tolkien's short stories occur in the same world, and if so at what time relative to the end of the Third Age.