Strengthening Local Transportation Security Capabilities Act of 2021 This bill addresses threat information sharing and law enforcement training regarding the enhancement of security for surface transportation assets. A surface transportation asset includes facilities, equipment, or systems used to provide transportation services by a public transportation carrier, railroad carrier, or an entity offering scheduled, fixed-route transportation services by bus. Specifically, the bill directs the Department of Homeland Security (DHS) to prioritize the assignment of officers and intelligence analysts from the Transportation Security Administration and the Office of Intelligence and Analysis to locations with fusion centers in jurisdictions with high-risk surface transportation assets to enhance the security of such assets, including by improving timely sharing of classified information regarding terrorism and other threats. The bill also authorizes DHS to develop a training program to enhance the protection, preparedness, and response capabilities of law enforcement agencies with respect to terrorism and other threats at a surface transportation asset.