There are a number of other Lamas in the Council of Lamas. They are tasked with finding the Dalai Lamas reincarnation. There is no next Dalai Lama, it is the same person just reincarnated over and over. A particular member of the council, Panchen Lama, is in charge of finding this reincarnation. There are various different techniques which have been used to find the Dalai Lama again but this is up to the Lamas and the search is done differently every time.
There is kind of a problem once the current reincarnation of Dalai Lama dies. Tibet is occupied by China who claims they have the responsibility of finding the Dalai Lama again. In 1995 Dalai Lama found the Panchen Lama but the Chinese government claimed he was wrong and pointed to another person as the Panchen Lama. The real Panchen Lama have not been seen again after this incident. Dalai Lama himself have claimed that the people might not want a Dalai Lama to lead them and that he will therefore take the form of an insect upon the next reincarnation.
Latest Answers