Veterans Improved Access to Care Act of 2021 This bill addresses the administration of the hiring process for Department of Veterans Affairs (VA) personnel. Under current law, the VA is required to publish on a VA website specified information related to staffing and the duration of the hiring process for certain health care appointees, such as physicians. The bill requires the VA Office of Inspector General to review the administration of such website annually instead of the current semiannual requirement. The VA must implement a two-year pilot program to assess the feasibility and advisability of expediting the Veterans Health Administration's onboarding process for new medical providers. Finally, the bill requires the VA to submit a strategy to reduce by half the duration of the VA's hiring process for licensed professional medical providers.