National Institute of Standards and Technology for the Future Act of 2021 This bill reauthorizes the National Institute of Standards and Technology (NIST) through FY2026 and establishes programs and activities. The bill sets forth requirements for supporting basic measurement science, technology research for engineering biology, biomanufacturing, and biometrology; developing standards to measure greenhouse gas emissions; carrying out research on identity management, cybersecurity, biometric identification, and communications measurement; assessing identified vulnerabilities with open-source software; operating the National Advanced Spectrum and Communications Test Network; a strategic plan concerning the Center for Neutron Research; establishing in NIST an organization to facilitate the development of forensic science standards; activities in support of green and sustainable chemistry (i.e., clean, safe, and economic alternatives, technologies, and methodologies to traditional chemical products and processes); information exchange and coordination among federal agencies and with the private sector to ensure federal engagement in the development and use of international technical standards; and establishing a five-year pilot program to award grants to support increased participation by small business and academic interests in international standards organizations. The Government Accountability Office must conduct a study of NIST's policies and protocols to protect its research and combat undue foreign influence. NIST shall establish, as a part of the Hollings Manufacturing Extension Partnership, a pilot program of expansion awards among manufacturing extension centers or a consortium of centers to develop and support training and job placement services. NIST shall establish a National Supply Chain Database to assist the federal government and industry sectors in minimizing disruptions to the United States' supply chain.