From LOTR.fandom.com :
Treebeard, also known as Fangorn, was the oldest of the Ents left in Middle-earth, an ancient tree-like being who was a “shepherd of trees”. He had a very tall and stiff-limbed appearance, with bark-like skin and leafy hair.
In Chapter Five of The Two Towers, Gandalf calls Treebeard “…the oldest living thing that still walks beneath the Sun upon this Middle-earth.” Later, Celeborn would address him as “Eldest.”
Treebeard was believed to be the oldest Ent who ever lived. He was so old that he remembered the time of Elves teaching the trees to speak, recalling how they wanted to talk to everything. In the time when Middle-earth was merely a giant forest, Treebeard roamed the land, presumably with his love, Fimbrethil. But after the loss of the Entwives, he and the remaining Ents dwelt in the Forest of Fangorn, isolating themselves from the outside world.
Treebeard’s ultimate fate is not known. While he aged very slowly and was extremely long-lived, he was not immortal. He most likely underwent the same fate of all the Ents: eventually settling down in one place, growing roots and leaves, and essentially becoming a tree himself, ceasing conscious thought.