Carhart made his television acting debut in NBC's 1978 mini-series The Awakening Land. Throughout the 1980s, Carhart made guest appearances on several television series, including Alfred Hitchcock Presents, Miami Vice and Crime Story. Carhart also appeared in two episodes of the crime drama Spenser: For Hire.

Two of Carhart's earliest film credits were the 1984 blockbuster horror comedy Ghostbusters and the independent comedy The Party Animal.

In 1985, Carhart had a supporting role in the Academy Award-winning drama Witness and the popular romantic comedy film Desperately Seeking Susan. In the former, he played a small but vital role as an undercover narcotics officer (Zenovich) whose brutal murder begins the story. His character is mentioned by name only once by Harrison Ford in the final script and he does not have any lines. Also in 1985, he appeared in the drama film Marie.

In 1986, Carhart worked on three films: Sweet Liberty, The Manhattan Project and Playing for Keeps.

In 1987, Carhart starred in a stage production of Don DeLillo's play The Day Room at the New York City Center. For his performance in this production, he was nominated for the 1988 Drama Desk Award for Outstanding Ensemble Acting.

He played the second male lead in the adventure drama The Rescue (1988) and the action comedy Pink Cadillac (1989). In addition, Carhart can be seen in the hit 1988 comedy film Working Girl.

In 1989, Carhart had a recurring role on the drama series Thirtysomething and was a regular on the CBS medical drama series Island Son.

His feature film credits expanded in the 1990s, with appearances in such hit films as The Hunt for Red October, Beverly Hills Cop III (1994), Black Sheep (1996) and Air Force One (1997). In 1991, he once again had a small but important role in another Academy Award-winning hit film, Thelma & Louise, playing Harlan Puckett, a drunk man who is shot dead by Louise Sawyer (played by Susan Sarandon) as he attempts to rape her friend Thelma Dickinson (played by Geena Davis) which kicks off the main plot.

Carhart has made guest appearances on a number of science fiction shows including in 1991 where he appeared in Quantum Leap, the time travel series starring Scott Bakula and Dean Stockwell. Later that year he appeared as Lieutenant Commander Christopher Hobson in the fifth-season premiere of Star Trek: The Next Generation, "Redemption (Part 2)". In 1995, Carhart was a guest star on the widely popular science fiction series The X-Files, appearing as Virgil Incanto in the episode "2Shy".

On Broadway, Carhart played Harold "Mitch" Mitchell in the 1992 revival of Tennessee Williams' A Streetcar Named Desire.

Between 2000 and 2003, Carhart played the recurring role of Eddie Willows on the hit CBS crime drama CSI: Crime Scene Investigation in four episodes. In 2002, he had a recurring role on the hit Fox series 24, playing Assistant NSA head Eric Rayburn in four episodes.

Carhart's most recent film was the 2005 direct-to-DVD Steven Seagal vehicle Black Dawn.

Carhart has also made guest appearances on shows such as The Practice, UPN's The Twilight Zone, Frasier, Judging Amy, Standoff and a 2007 episode of Law & Order: Criminal Intent entitled "Silencer".