In 1986, Clohessy moved to Los Angeles to work in film and television, and landed a regular role as a relatively green policeman on the final season (1986-87) of NBC heavy hitter "Hill Street Blues" The actor then made his feature debut playing a detective in the thriller "The Believers" (1987). Evidently quite believable as an agent of the law, Clohessy returned to series television, playing the short-tempered young detective opposite Pat Morita's calm veteran from 1987 to 1988 on the ABC series "Ohara". A 1988-89 recurring stint as a priest on NBC's "Tattinger's" passed some time until he was cast in "One of the Boys" (NBC, 1989), starring opposite Maria Conchita Alonso's immigrant bookkeeper eager to learn the ways of the construction business. It turned out that Alonso's character and Clohessy's contractor were married soon into the run of the series, but the pair didn't get much past the honeymoon before the plug was pulled on the show. Playing the husband of "Laurie Hill" didn't offer much in the way of job security either; the ABC show was cancelled not two months after its 1992 debut.
Clohessy acted in the popular family film "Angels in the Outfield" in 1994, and was featured that same year in the racism-themed, fact-based period piece "Assault at West Point" (Showtime). A guest role as a detective who is taking out his job stresses on his wife in a domestic violence plot on Tom Fontana's acclaimed drama series "Homicide: Life on the Street" (NBC) showed a darker side to an actor previously identified with tough-acting nice guys. A two-episode arc on CBS' "Chicago Hope" kept Clohessy in the public eye, while a co-starring turn opposite Jaclyn Smith in the cliched Family Channel TV-movie "Married to a Stranger" showed he could play a supportive and somewhat stiff straight man and still break the audience's collective heart. After this twelve-year stint in Los Angeles, Clohessy packed up his family and returned to NYC, promptly landing a guest role on NBC's "Law & Order".
In 1999, Clohessy introduced the fair-minded corrections officer Murphy into the fray at "Oz", drafted by Fontana for his sports know-how. A former heavyweight Golden Gloves contender, Clohessy was the perfect choice for the part of Murphy, the officer who would oversee the prison's ultimately ill-fated boxing tournament. Continuing his role on "Oz", and given the freedom of the series' eight episode seasons, Clohessy also stayed active on stage, most notably playing Mitch in a 1998 Hartford Stage production of "A Streetcar Named Desire" and taking a co-starring role in the Yale Repertory Theater presentation of Canadian playwright George F Walker's "Heaven" in 2000.