National Biosecurity Improvement Act of 2021 This bill requires the Government Accountability Office to study and report to Congress about policies and past actions of the National Institutes of Health related to enhancing potential pandemic pathogens and similar research that could result in unintended homeland and national security concerns. Among other matters, the study must address how federal agencies ensure that such research is conducted safely and without compromising national security and the extent to which agencies consider national security information in decisions about whether to fund research in other countries.