Terrorism Risk Insurance Act of 2002 Reauthorization Act of 2013 or the TRIA Reauthorization Act of 2013 - Amends the Terrorism Risk Insurance Act of 2002 to extend the Terrorism Insurance Program until December 31, 2019 (under current law the Program expires on December 31, 2014). Requires the Secretary of the Treasury to collect all required terrorism loss risk-spreading premiums for any act of terrorism that occurs on or after January 1, 2012, by September 30, 2024 (currently, by September 30, 2017).