Father Time

"That is old Father Time, who was once a King in Overland. Now he has sunk down into the Deep Realm and lies dreaming of all the things that are done in the upper world. Many sink down and few return to the sunlit lands. They say he will wake at the end of the world."

- Mullugutherum

Biography
Father Time was the "giant of giants" who once ruled a kingdom in Overland. At some point he sank down into Underland and was sleeping there, along with Birds, Bats, Lizards and Dragons in another cavern, dreaming of the goings on of the overworld, when Eustace Scrubb, Jill Pole and Puddleglum were on their quest to find Prince Rilian. The narration says that "his face was not like a giant's, but noble and beautiful." He had a large beard which covered him to his waist.

It is unknown what happened to him when Underland fell apart, although he presumably carried on sleeping.

"While he lay dreaming his name was Time. Now that he is awake he will have a new one."

- Aslan

When the end of the world came Aslan called "Time" several times, which woke him up. He then helped Aslan end the world: in particular he destroyed the sun by squeezing it like an orange in his hand, which brought an end to all ages. He was then given a new name, and left outside at the end of the world. He did not enter Aslan's Country, and what happened to him afterwards, is unknown, but it's presumed that he froze to death and his soul joined the souls of the creatures that helped him destroy Narnia.