Bringing Low-cost Options and Competition while Keeping Incentives for New Generics Act of 2021 or the BLOCKING Act of 2021 This bill modifies provisions related to market exclusivity for a generic drug. Currently, the Food and Drug Administration (FDA) awards 180 days of exclusivity on the market to a first applicant to file a qualifying application for market approval of a generic drug. Generally, this exclusivity period begins upon a first applicant's commercial marketing of the drug. The bill authorizes the FDA to approve a subsequent generic drug application prior to a first applicant's first date of commercial marketing if (1) the subsequent application is ready for full approval, (2) a first applicant's application has been pending for at least 30 months, and (3) the approval of a first applicant's application is not precluded by patent infringement claims asserted against that first applicant.