Assisting Community Colleges in Educating Skilled Students to Careers Act of 2021 or the ACCESS to Careers Act of 2021 This bill requires the Department of Education (ED) to award competitive grants to community and technical colleges and to states for education and career training programs and related activities. Specifically, the bill requires ED to award grants to community and technical colleges and consortia of such colleges to (1) carry out student support services, such as child care, transportation, direct financial assistance, and case management services; and (2) carry out certain program activities, such as developing programs that accelerate learning, expand career pathways to postsecondary credentials, or expand dual or concurrent enrollment programs. Additionally, ED must award grants to states to establish statewide systemic reforms that support education and career training programs. States receiving these grants must (1) use funds to implement statewide policies, such as policies to support the expansion of education and career training programs for in-demand industry sectors or occupations, and (2) provide subgrants to community college partnerships to carry out program activities and student support services. Further, ED must (1) contract with an independent third party to perform an evaluation of the grants awarded under the bill, (2) provide technical assistance, and (3) submit an annual report to Congress.