Keeping Gun Dealers Honest Act of 2021 This bill modifies the requirements and penalties applicable to an individual who engages in the business of dealing, importing, or manufacturing firearms (i.e., a federal firearms licensee, or FFL). Among other things, the bill does the following: increases the allowable number of annual compliance inspections; authorizes the Bureau of Alcohol, Tobacco, Firearms and Explosives (ATF) to hire at least 80 additional personnel to conduct additional inspections; increases the maximum prison term for an FFL or licensed collector who knowingly makes a false statement or representation in required firearms records; allows the ATF to require an FFL to conduct physical inventories if the FFL unlawfully transfers a firearm or if 10 or more crime guns are traced back to the FFL; allows the ATF to deny an application for a federal firearms license if it would endanger public safety or if the applicant is unlikely to comply with the law; and modifies the liability standard for an FFL who fails to comply with laws or regulations.