Terrorist Firearms Prevention Act This bill authorizes the Department of Justice (DOJ) to deny the transfer of a firearm or explosive, or the issuance of an explosives license or permit, to known or suspected terrorists. Specifically, DOJ may deny a transfer to, or deny a license or permit for, an individual who is included on the No Fly list or the Selectee list. The No Fly and Selectee lists are subsets of the Terrorist Screening Database—the U.S. government's consolidated database of individuals known or reasonably suspected to be involved in terrorist activities. DOJ and federal, state, and local law enforcement must be notified immediately of requests to transfer a firearm or explosive to a person who is, or in the last five years was, identified on the database. The bill establishes a judicial review process for appealing a denial by DOJ.