Foreign Agents Registration Modernization Act of 2021 This bill modifies requirements related to the electronic database that contains the registrations that an agent of a foreign principal must file with the Department of Justice (DOJ). Specifically, DOJ must establish and maintain the free and publicly accessible National Foreign Agents Database, which must make such foreign agent registrations searchable, sortable, and downloadable. The database must also make filed registrations and supplements immediately available for public inspection. (Currently, DOJ is required maintain a database with these features, but only to the extent that the features are technically practicable.) The database must also meet federal standards for making digital information accessible to individuals with disabilities.