A student of the trombone and the piano, Tompa got into arranging, orchestrating and conducting during his high school years. He completed his BA and MA studies in orchestral conducting at the Franz Liszt Academy of Music in Budapest. In the meantime, he also attended orchestrating and arranging masterclasses held by the likes of Sammy Nestico, Gordon Goodwin, John Clayton, Jonathan Tunick, Larry Blank and Callum Au. As a conductor he has worked with the Hungarian National Opera, the Bucharest National Opera and the Hungarian Radio Symphony among others in Hungary, Romania and the Czech Republic. Since 2023, Tompa has been a conductor and session producer at Budapest Scoring. He has recorded for artists and composers such as Danny Elfman, Paul Anka, David Foster, Andrea Bocelli, Vince Mendoza, Lorne Balfe, Bill Ross, Chris Walden and Bear McCreary. He has conducted the soundtracks of series such as Wednesday, Squid Game, Outlander, FUBAR and Palm Royale, working with the likes of Disney, Netflix, HBO, Amazon Prime, Universal, Apple TV, Sony Playstation, CNN and the BBC. As an orchestrator and arranger he has collaborated with a number of theaters (most notably in the 2021 production of "Cabaret" at the Comedy Theater of Budapest), as well as Hungarian pop and jazz artists. In 2021 he founded Budapest Orchestra Project, and to this day remains the ensemble's music and artistic director.