Quad Critical Minerals Partnership Act This bill requires the President to establish a comprehensive strategy to address the national security threat posed by China's dominant share of the global critical minerals market by developing a more reliable and secure supply chain of critical minerals. The bill also requires the U.S. International Development Finance Corporation to prioritize projects that will support the strategy, including projects that will facilitate cooperation with other countries in the Quadrilateral Security Dialogue on investments related to critical minerals. (The dialogue is a coalition comprised of the United States, Japan, India, and Australia.) The U.S. Trade Representative must initiate multilateral discussions with other countries in the dialogue to support the strategy and facilitate cooperation on investments related to critical minerals.