For the first two years of its existence, the English didn't recognize it as a state. They recognized it as part of Occupied China. In 1974, however, they realized that it was no threat to themselves, and realized its independence.
Tibet was a Buddhist Theocratic Republic, with the Dalai Lama as supreme ruler. The reason it was technically a republic is because Tibet itself was divided into four separate regions. The people got to vote a governor of each, but they all still had to answer to the Dalai Lama.