Cleve Broch made his film debut in 1995, in the Swedish-Norwegian coming-of-age film Sebastian. In 2002, Cleve Broch became well known for playing Roger, a kindergarten Teacher, on NRK's 2002 drama series Lekestue. Critics praised him for his "dreamlike charisma" and "expressive, awkward, body language", and he was nominated for an award in the category "Best male actor" in Gullruten for his performance. The following year, Cleve Broch got his big break in Buddy, a romantic comedy directed by Morten Tyldum. The film revolves around two friends, played by Cleve Broch and Aksel Hennie, and their ascent from being billboard hangers to getting their own segment in a popular talk show. According to Cleve Broch, "it was a challenge to make all the storylines affect my character and the way he sees things". The film was well received by critics, who highlighted its "perfect cast", and were impressed with what was coined a "new generation of [Norwegian] film actors".

Cleve Broch received his education at the Norwegian National Academy of Theatre from 1996 to 1999. He made his debut in the play Hjalmar og Frode. From 2005, Cleve Broch has been at Nationaltheatret, where he has portrayed Julian the Apostate in Henrik Ibsen's Emperor and Galilean. He has previously been employed at Oslo Nye Teater and Det Norske Teatret, where he has appeared in plays such as The Seagull by Anton Chekhov, and Who's Afraid of Virginia Woolf? by Edward Albee. Cleve Broch was named "Theatre Talent of the Year" in 2002 by Dagbladet.

In 2004, Cleve Broch took on another film role alongside Aksel Hennie, this time in Uno (2004), a drama set in a shady gym in Oslo. Cleve Broch plays Morten, the best friend of David (Hennie). The film was a critical success. Verdens Gang and Dagbladet both rated it 5 out of 6, while Birger Vestmo of NRK P3 gave it 6/6. Vestmo praised Cleve Broch for believably portraying the cowardly Morten, while Adresseavisen commended Cleve Broch and Hennie for their "spontaneous interplay". In 2006, Cleve Broch starred opposite Ane Dahl Torp in Uro, a crime film directed by Stefan Faldbakken. His portrayal of the undercover police officer Hans Petter "HP" Hansen was generally well received. Nettavisen's reviewer felt that Cleve Broch carried the film, and praised him for "brilliantly unfolding Hans Petter's troubled mind". Both he and Dahl Torp were nominated for Amanda Awards, for "Best Leading Actor" and Best Leading Actress", respectively.

Cleve Broch once again starred alongside Hennie in Max Manus, a 2008 war film based on real events from the life of resistance fighter Max Manus, played by Hennie. Cleve Broch portrays Gregers Gram, fellow resistance fighter and best friend of Manus. Cleve Broch found it easy to play Hennie's best friend. "Once, many years ago, we were going to play friends, and while preparing for that, we hung out together every day for a whole summer", he recalled. In an interview on TV 2, he expressed pride that he performed all the Stunts himself. In preparation for the film, the actors got to fire live ammunition, something "one rarely gets to do" in Norwegian film, according to Cleve Broch. He was once again critically lauded for his on-screen interactions with Hennie, particularly for being able to emphasize the special friendship and humour between Manus and Gram. He received an Amanda Award nomination in the category "Best Actor in a Supporting Role" for his performance.