Jobs for Economic Recovery Act of 2021 This bill establishes an employment and training program to assist workers who are unemployed or underemployed due to the COVID-19 pandemic, and other displaced workers and those who face barriers to employment, to obtain employment, including through subsidized employment programs. Specifically, states, Indian tribes, local governments, and particular nonprofits must meet certain conditions before receiving funding to establish these programs. In addition to providing this funding, the bill requires the Department of Health and Human Services (HHS) to award temporary grants to these entities to plan and implement the programs. The HHS Inspector General must biennially audit a sample of the state programs to ensure compliance with program and nondisplacement requirements, and to identify and protect against any waste, fraud, or abuse in such programs. HHS must make information publicly available to job seekers online about whether they are eligible for state, local, or tribal program employment services, and the agency to contact for further information. The bill also creates an employee retention work opportunity tax credit for employers that retain workers hired through the program for 24 months. Finally, the bill requires the Government Accountability Office to evaluate whether the retention credit (1) had a meaningful impact on retention as compared to currently existing and previous subsidized employment programs, and (2) was easily understood by employers and had an impact on hiring decisions in addition to any subsidy received by this bill.