To add to the other answers, the Dalai Lama is a Buddhist teacher, yes, one of many from Tibet. Unusually he had a secular role as well, as head of the country but he has renounced that now.

As Alex Zendo said, Buddhists don’t have any spiritual leader for Buddhism as a whole. There is no no spiritual leader even for the main schools of Tibetan Buddhism. There are many Buddhist teachers from Tibet and there are Western teachers now recognized as able to teach in the same traditions. As a Buddhist practicing in the tradition, you might have any of these as your main teacher or teachers and you may have many teachers.

However, it’s not at all like the Pope, where the Pope can make proclamations and resolve spiritual issues for the Catholic Church (if I understand right). The Dalai Lama can’t change a word of the Buddhist teachings, nor does he have any authority over what other Buddhist teachers teach. He can’t tell Tibetan Buddhists what to do. He can give more detailed personal advice to his own students, but when, for instance, the Chinese ask him to say that Tibetan Buddhists should do x or y, that’s just not something that is part of his role. He could say such things, but there would be no obligation on any Buddhist to do what he says, and they wouldn’t be expected to. So this is an impossible request. What he can do is to present his understanding of the Buddhist teachings, and especially, his understanding of them in the Tibetan Buddhist traditions which he has a deep knowledge of. But in this he has no priority over any other Buddhist teacher.

The four main traditions of Buddhism do have teachers who are heads, but their role is mainly administrative at least compared with Western ideas of the leaders of a religious group, and ceremonial, passing on blessings that they in turn have received from their teachers.

Also there are many different styles and ways of practicing the path of the Buddha. You find your own path, you connect to the truth as best you can, and you listen to the advice of those you consider to be wise, and you put what they say into practice and judge the advice by how it works in practice. That’s Buddha’s instruction in the sutras.

He is a recognized reincarnation of the previous Dalai Lama which means he was recognized as a young boy - but he has no hereditary or other connection with the previous Dalai Lamas. He was just a child of a small farmer in a remote subsistence village in Tibet. The method Tibetans use for choosing a new Dalai Lama only makes sense if you believe in rebirth.

Also, there’s no idea there that he would be the “same personality” as the previous Dalai Lama. The present day Dalai Lama is scholarly with a deep understanding of the Tibetan Buddhist sutras and teachings, passed his Lharumpa degree as a young man in his early 20s (it usually takes 15 years). He has studied all four of the main Buddhist traditions in Tibetan Buddhism. He is also a Buddhist monk. Previous Dalai Lamas were different in personality and not all of them were scholars. The sixth Dalai Lama particularly was a poet, a bit like the Western William Blake, whose poems are still enjoyed to this day by Tibetans and he handed back his novice monk’s robes as a young man.

The Dalai Lama and the Panchen Lama are connected - the Dalai Lamas recognize and help to locate the young Panchen Lamas and vice versa. But when our current Dalai Lama recognized the young Panchen Lama, the Chinese removed him for safe keeping making him the youngest political prisoner at age 6 and installed their own selection for the Dalai Lama instead.

Photograph of the Panchen Lama Gedhun Choekyi Nyima aged six. The Chinese took him into custody soon after, as a six year old, saying it is for his own protection.

If he is still alive he is now aged 28. The Chinese say he is still alive and well and living a normal life, but they have not permitted anyone outside of China to communicate with him and won’t say where he is in China.

The Dalai Lama says he hasn’t decided yet whether to have another recognized rebirth when he dies. If he doesn’t, this may be our last Dalai Lama. If he does, understandably, he has said that he won’t take rebirth in China. So far all the Dalai Lamas have been men, but when asked he has said that the next Dalai Lama could be a woman.

If this is our last Dalai Lama, he would still take rebirth, but his next rebirth would not be recognized, so would have no way to know that he or she was the Dalai Lama in a previous life (unless she or he had the ability to see past lives like the Buddha).