He is the founder of the jazz section at the Faculty of Music in Belgrade, at which he was a visiting professor and music advisor (2012- 2018). He has worked as a university professor in Graz, as well as a visiting professor at the University of New Hampshire, Department of Music (2002- 2010). On several occasions, he has also taught at the Royal Conservatory of Hague, Rotterdam Conservatory, Conservatorium Van Amsterdam, Paris Conservatory, the New School of Music in New York, and other music faculties around the world.

Stjepko was born in 1950 in Ruma. He studied at the Faculty of Music in Belgrade, the Swiss Jazz School in Bern, and Boston Conservatory at Berklee.

He was a trumpet player and soloist of the Jazz Orchestra of the Radio Television of Belgrade (today’s RTS Big Band), a co-leader of Gut- Marković sextet, the most famous jazz ensemble in former Yugoslavia, a member of the Trumpets and rhythm Unit Gojković-Kovačev, and the Stjepko Gut jazz quintet Sketches of Balkan. He was also a member of the Lionel Hampton All Star Big Band, as the only Caucasian musician (1980-1981), the SFB Big Band Berlin, Ernie Wilkins Almost Big Band, Clark Terry Big Band (1994-2010), the Trumpet Summit 1990. Marciac Friends. He has worked with many European jazz ensembles and Big Bands.

He has performed at jazz festivals, concerts and tours all around the world along with some legendary jazz artists such as: Clark Terry, Johnny Griffin, Jimmy Heath, Mel Lewis, Horace Parlan and many more.

He has played at many eminent jazz festivals, including the North Sea Jazz Festival, the JVC Jazz Festival in New York, Havana Jazz Festival. He has also performed at jazz festivals around the territory of former Yugoslavia, as well as on prestigious stages, such as the Apollo Theatre in New York, the Blue Note in New York, the Village Vanguard in New York, and others.

He has recorded numerous studio albums under his name, and as a part of different music formations. He is the composer of the Serbian Symphony Jazz Suite, written for the symphony orchestra, choir and jazz quartet and premiered in 2011.

His most notable albums are: Gut-Marković sextet, Sketches of Balkan by the Stjepko Gut sextet, two albums with the RTS Big Band, Mr C.T, and Afro-Balkan Sketches.