Energy Security Cooperation with Allied Partners in Europe Act of 2021 This bill establishes requirements related to U.S. international energy strategy. Applications to export natural gas to North Atlantic Treaty Organization (NATO) member countries, Japan, and certain other countries shall be granted on an expedited basis without modification or delay. The President shall impose sanctions on a person that provides certain equipment, investment, or services to the Russian government or related entities for constructing or servicing Russian energy export pipelines. The Department of State shall report to Congress on a strategy to enhance the energy security of NATO member countries and increase U.S. energy exports to such countries.