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 grants 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 shall (1) seek to establish a U.S. consulate in Lhasa, Tibet; (2) establish a Tibet section in the U.S. embassy in Beijing; (3) make diplomatic efforts on issues such as water security in the region; and (4) encourage Nepal to provide legal documentation to certain Tibetan residents in Nepal. The State Department shall not authorize any additional Chinese consulates in the United States until the U.S. consulate in Lhasa is established. 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 also adds China-related topics to an existing annual report on international religious freedom.