His mother, Kristin Linklater, was a Scottish-born Professor of Theatre and Chair of the Acting Division at Columbia University and a teacher of vocal technique.

In July 2006, Linklater appeared in Keith Bunin's The Busy World Is Hushed opposite Jill Clayburgh off-Broadway at Playwrights Horizons.

He played the title character in Hamlet at South Coast Repertory in Costa Mesa, California and the Long Wharf Theater in New Haven, Connecticut.

[7] He appeared in The Public Theater's 2009 production of Twelfth Night at Shakespeare in the Park as Sir Andrew Aguecheek, opposite Anne Hathaway, Audra McDonald and Raul Esparza.

He made his Broadway debut in October 2011 in Theresa Rebeck's new play Seminar opposite Alan Rickman, Jerry O'Connell, Lily Rabe, and Hettienne Park.

Also in 2017, he had a small role in the third season of the FX black comedy crime drama series Fargo, created by Legion showrunner Noah Hawley.

In 2020, Linklater was cast in the Amazon Prime series Tell Me Your Secrets as John Tyler, a convicted rapist seeking redemption by trying to find a missing girl.

In 2022, Walter Hill's western Dead for a Dollar premiered at Venice Film Festival and in the United States, with Linklater playing wealthy villain Martin Kidd.