Protecting American Innovation and Development Act of 2021 This bill authorizes import controls against certain foreign persons that infringe patents belonging to a U.S. person that are essential to a wireless communications standard. Specifically, the Department of Commerce must create a list of foreign entities that are citizens or nationals of a country of concern and that engage in the unlicensed use (i.e., infringement) of such essential wireless communications patents. A country of concern is a country wherein the persistent infringement of these patents poses a threat to (1) U.S. wireless communications research and development infrastructure, and (2) U.S. national security. Any foreign entity on this list, as well as specified persons that raise a national security concern with respect to wireless communications technology, may be subject to import controls (for example, a foreign entity may be required to post a bond before importing into the United States any goods that potentially infringe the wireless patent in question). Commerce must also establish a watch list of foreign entities from a country of concern that (1) are selling in the United States a product claiming to comply with a wireless standard, and (2) have not obtained a license (or taken certain actions to obtain that license) for patents essential to that wireless standard. An entity on either list may petition Commerce to be removed from that list on the basis that the conditions that led to its inclusion no longer exist.