Dairy Pricing and Policy Commission Act of 2021 This bill directs the Department of Agriculture (USDA) to temporarily establish the Dairy Pricing and Policy Commission. The commission shall develop legislative, regulatory, and market-based recommendations to improve milk prices and dairy farm profitability, including for responding to periods of heightened dairy production during low prices; enhance competitiveness of American dairy in world markets; and evaluate new markets for dairy exports. The commission shall terminate on the earlier of (1) the date it submits to USDA and Congress a report of its legislative and regulatory recommendations; or (2) the date that is two years after the commission's establishment.