Corbin began his career as a Shakespearean actor in the 1960s, but today he is more likely to be seen in the role of the local sheriff, military leader, or some other authority figure, though on occasion, he has effectively portrayed murderous villains, as well. To moviegoers, he is well remembered as General Beringer in WarGames, John Travolta's uncle Bob Davis in Urban Cowboy, co-starring with Clint Eastwood in Any Which Way You Can, or Roscoe Brown, July Johnson's bumbling deputy in the acclaimed Western Lonesome Dove.

In 1983–1984, Corbin played Merit Sawyer in the NBC television series Boone. Corbin's role was that of a stern father to the young actor Tom Byrd, who played Boone Sawyer, an aspiring singer. The program was set in rural Tennessee during the 1950s and was created by Earl Hamner, who had great success earlier with CBS's The Waltons.

In 1994, Corbin narrated the acclaimed TBS documentary MoonShot, telling the story of the 1960s space race from the first-person viewpoint of Mercury Seven astronaut Deke Slayton. In 2007, he played the character Clay Johnson, father of Deputy Chief Brenda Leigh Johnson on The Closer series.[5] In 2003, Corbin co-starred with Northern Exposure castmate John Cullum in Blackwater Elegy, an award-winning short film written by Matthew Porter and co-directed by Porter and Joe O'Brien.From 2003–2008, Corbin played Whitey Durham, the basketball coach for the Tree Hill Ravens on The WB/CW teenager drama series One Tree Hill.[5] He also had a role in 2007's Oscar-winning film No Country for Old Men.In 2014, Corbin worked with Tracey Birdsall[7] on Dawn of the Crescent Moon,[8] followed by working alongside her for the science fiction films At the Edge of Time (2016)[9] and The Time War (2017).[10]

In 2020, Corbin had a recurring guest role as Everett Acker in Better Call Saul.