Promoting Free and Fair Elections Act This bill prohibits federal agencies from using funds made available for salaries and expenses to solicit or enter into agreements with nongovernmental organizations to conduct voter registration or voter mobilization activities on the agency's property or website. The bill also requires federal agencies to delay carrying out certain activities pursuant to Executive Order 14019 (which established requirements for expanding access to voter registration and election information) until various conditions are met, such as the agency submitting reports to Congress. The bill also prohibits institutions of higher education that operate federal work-study programs from registering or mobilizing voters on or off campus.