The Chinese are expected to probably dictate who the next Dalai Lama is.
It works by a boy being recognized as the reincarnation, and the Chinese have declared that all senior religious officials in the religion must be approved by them.
For the #2 position in the religion, they already did this. They picked a boy themselves and named him to the position. The boy the Tibetans named and view as the legitimate person was taken into 'protective custody' by the Chinese in 1995 (with his family IIRC) and has not beeen heard from. THe US and Europe have asked the Chinese for guarantees of his safety and the Chinese refuse. The Tibetans do not recognize the Chinese selected person.
THe current Dalai Lama has said the next Dalai Lama, if there is one - it might be put to a vote whether to have another - will not be in any non-free country, including Tibet controlled by China.
This is to preclude the Chinese from naming the next Dalai Lama.