Operation Warp Speed Act of 2021 This bill modifies procedures for Emergency Use Authorization (EUA) and provides additional authority to the Department of Health and Human Services (HHS) for vaccine production in response to a public health emergency. It also makes changes to the administration of the Strategic National Stockpile. (An EUA temporarily authorizes use of an otherwise unapproved medical product or device in certain emergency situations.) Among other modifications, the bill places additional requirements on EUA approvals. Specifically, HHS may only approve an EUA if, after consulting four specified agencies, at least three of them vote to grant approval. Currently, HHS's authority to approve an EUA, which it has delegated to the Food and Drug Administration, is not limited by the votes of consulting agencies. Additionally, the bill authorizes the use of HHS funds to produce a vaccine before it is licensed or authorized in response to a public health emergency. The bill also establishes the Office of Operation Warp Speed within the HHS Office of the Assistant Secretary for Preparedness and Response to expedite the production of vaccines and medical countermeasures to respond to public health emergencies. With respect to the Strategic National Stockpile, HHS must assess, as part of its annual threat-based review, the levels of and supply chains for materials in the stockpile. HHS must also give priority to domestic manufacturers when procuring materials for the stockpile. If materials cannot be sourced domestically, HHS must give priority to manufacturers that are not located in China.