Protecting Election Administration from Interference Act of 2021 This bill revises preservation and retention requirements for federal election records. It also revises criminal penalties related to election records and the voting process. Under current law, election officials must, for a period of 22 months from the federal election, retain and preserve all election-related records and papers. This bill extends the requirement to electronic records and electronic equipment. Next, the bill directs the Cybersecurity and Infrastructure Security Agency to issue minimum standards and best practices for retaining and preserving records (including electronic records), papers, and electronic equipment, including protocols for observing their preservation, security, and transfer by the Department of Justice (DOJ) and a representative of each political party. In addition, the bill revises the federal criminal offense related to election records or papers to include reckless disregard of election record requirements resulting in the theft, destruction, concealment, mutilation, or alteration of a record, paper, or electronic equipment. Further, the bill allows DOJ to demand electronic records and electronic equipment for inspection and generally prohibits DOJ from disclosing this information. The bill allows DOJ and candidates for federal office to bring an action in a district court to compel compliance with election record requirements. Finally, the bill extends criminal penalties related to voting interference to include intimidating, threatening, or coercing (or attempting to do so) an individual for processing or scanning ballots, tabulating, canvassing, or certifying voting results.