Morse has stated that out of all of the films he has done, his favorites are "The Green Mile", "The Crossing Guard", and "The Indian Runner". In 2010, he guest starred in two episodes of the HBO drama series "Treme", as Lt. Terry Colson of the New Orleans Police Department. He was promoted to series regular starting with the show's second season, which began in April 2011. Later that year, Morse won the best actor award at the Karlovy Vary International Film Festival for his role in "Collaborator". He played an ex-CIA agent in the film "World War Z" (2013). He played the late NFL player, Mike Webster, in the biographical sports drama "Concussion".