Quantum Network Infrastructure and Workforce Development Act of 2021 This bill supports research in quantum networking and communications. The Quantum Networking Working Group within the Subcommittee on Quantum Information Science of the National Science and Technology Council shall submit to Congress a report that has a plan for the advancement of quantum networking and communications technology in the United States. The National Institute of Standards and Technology shall carry out research to facilitate the development and standardization of quantum networking and communications technologies and applications. The Department of Energy shall supplement the Energy Sciences Network User Facility with dedicated quantum network infrastructure to advance development of quantum networking and communications technology. The National Science Foundation (NSF) shall enter into an agreement with the National Academies of Sciences, Engineering, and Medicine to study ways of supporting the next generation of quantum leaders. The NSF shall prioritize the better integration of quantum information science and engineering into the science, technology, engineering, and mathematics (STEM) curriculum for each grade level from kindergarten through grade 12. The NSF shall carry out the Next Generation Quantum Leaders Pilot Program to provide funding for the education and training of the next generation of students in the fundamental principles of quantum mechanics.