College Equity Act of 2021 This bill requires the Department of Education (ED) to establish grant programs for reviewing and addressing inequities in student recruitment, admissions, and support at institutions of higher education (IHEs). Specifically, ED must award grants to IHEs to conduct equity audits that review IHEs' policies, practices, and resources (e.g., admission policies, financial aid, and faculty diversity) to identify areas that might produce gaps in access and outcomes by certain factors. These factors include, among others, gender, race, ethnicity, national origin, and age. In addition, ED must award grants to IHEs for executing improvement plans that address inequities. Finally, higher education accrediting agencies and associations must assess the findings from the audits and assist IHEs in addressing inequities.