Pell Grant Preservation and Expansion Act of 2021 This bill makes various changes to the Federal Pell Grant program, including by expanding student eligibility for Pell Grants. The bill also revises student eligibility for federal student-aid programs. Specifically, the bill provides funding to increase the maximum Pell Grant award for each eligible student. Further, the bill requires the award amount to be adjusted for inflation. Next, the bill allows students who receive means-tested federal benefits (e.g., Medicaid) to automatically qualify for the maximum Pell Grant award plus an additional award amount. In addition, the bill moves the Iraq and Afghanistan Service Grant program into the Pell Grant program. Next, the bill raises from 12 to 18 the total number of semesters during which a student may receive a Pell Grant. The bill makes Dreamer students (i.e., students who have been granted Deferred Action for Childhood Arrivals status) who entered the United States before the age of 18 and who meet certain educational criteria eligible for federal financial aid. The bill also revises satisfactory academic progress requirements for federal student-aid programs, including by allowing a student who has not been enrolled in an institution of higher education for two years to regain eligibility for federal student aid.