He moved to the United States in October 2006 where he studied at the American Musical and Dramatic Academy in New York. He graduated in February 2008.
While appearing as Marchbanks in George Bernard Shaw's Candida at the Irish Repertory Theatre, New York, in April 2010, Underwood was asked to play the part of Alan Strang in a production of Equus at the John Drew Theatre, East Hampton, co-starring alongside Alec Baldwin.
In 2013, Underwood was cast in the eighth season of television series Dexter in the recurring role of Zach Hamilton, Dexter Morgan's "protégé". He subsequently joined the third season of Homeland as Leo Carras.
Beginning in February 2014, Underwood took on the dual roles of twins Mark and Luke Gray in the second season of the Fox murder mystery The Following. But after the death of Luke, he was left playing Mark - who had split identities - in its third and final season.
Underwood married Actress Valorie Curry in Summer 2016.
As of 2017, Underwood joined the cast of the hit AMC thriller series Fear the Walking Dead in its third season as Jake Otto, the enigmatic son of the colony leader.