Health Force, Resilience Force, and Jobs to Fight COVID-19 Act of 2021 This bill establishes and expands programs to bring on individuals to perform public health functions, such as contact tracing and vaccine administration, to respond to the COVID-19 (i.e., coronavirus disease 2019) emergency and meet future public health needs. The bill provides funding for the Centers for Disease Control and Prevention (CDC) to establish a Health Force. The funds are designated as an emergency requirement, which exempts the funds from discretionary spending limits and other budget enforcement rules. To establish the force, the CDC must award grants within 30 days to state, tribal, territorial, and local governments and community health centers to recruit and train individuals for roles in public health and health care. The Federal Emergency Management Agency (FEMA) must hire and train additional individuals for its Cadre of On-Call Response/Recovery Employees. These employees may be detailed to certain federal agencies or to state, local, or tribal governments to support response efforts related to COVID-19 or other disasters or emergencies.