The 14th Dalai Lama will remain the spiritual leader of the Tibetan people (technically the head monk of Tibetan Buddhism), a title he has held since he was two and declared the reincarnation of the 13th Dalai Lama by a group of Buddhist monks. He will remain the Dalai Lama until his death.
According to Tibetan tradition, when a Dalai Lama dies, a group of monks goes out in search of his reincarnation, which will be a child who is born around the same time. It can sometimes take a couple years to find that child.