Essential Medicines Strategic Stockpile Act of 2021 This bill requires the Department of Health and Human Services (HHS) to create a pilot program with private entities to test the effectiveness of acquiring, maintaining, managing, and distributing a stockpile of generic drugs at risk of shortage. Specifically, HHS must enter into contracts of up to three years for entities to create a six-month stockpile of up to 50 types of such drugs. The bill establishes various program requirements, including annual evaluations by the Government Accountability Office.