Original: For certain periods of time between the 17th century and 1959, the Dalai Lamas sometimes directed the Tibetan Government, which administered portions of Tibet from Lhasa. The 14th Dalai Lama remained the head of state for the Central Tibetan Administration ("Tibetan government in exile") until his retirement on March 14, 2011.
Simplified: Between the 17th century and 1959, the Dalai Lama was the head of the Tibetan government.