Tibetan Policy and Support Act of 2019 This bill modifies and reauthorizes various programs and provisions related to Tibet and China. The President shall provide funds to nongovernmental organizations for projects supporting Tibetan communities in Tibet in areas such as sustainable economic development, cultural preservation, and education. The Department of State may not authorize any new Chinese consulates in the United States until a U.S. consulate has been established in Lhasa, Tibet. The bill reauthorizes the Office of the U.S. Special Coordinator for Tibetan Issues and expands the office's duties to include additional tasks, such as pursuing international coalitions to ensure that the next Dalai Lama is appointed solely by the Tibetan Buddhist faith community. The bill requires the State Department to discuss U.S. efforts to promote the human rights of the Tibetan people, including the right to select and venerate their own religious leaders, in an existing periodic report on Tibet.