[2] Hrůša studied piano and trombone, and developed an interest in conducting, during his years at Gymnázium třída Kapitána Jaroše in Brno.
While at school he had lessons with an experienced repetiteur and conductor at the National Theatre in his home city, Evžen Holiš, where he got know the work and atmosphere of an opera house.
[2] When 18 he entered the Academy of Performing Arts in Prague, where his teachers included Jiří Bělohlávek (from his second year) for conducting,[3] Radomil Eliška and Leoš Svárovský.
"[2] Hrůša's first conducting position after graduation was when he was at the Bohuslav Martinů Philharmonic orchestra of Zlín, with which he went on tour to Spain in 2004 - during long bus trips, he and the players were able to bond before he took up his post officially in 2005.
[2] He also began to build up his experience in the Czech Republic, where he conducted The Cunning Little Vixen in 2005 and Marcel Mihalovici's Krapp, or The Last Tape, at the National Theatre in Prague.
[8] However, in January 2012, in the wake of the resignation of Keith Warner from the artistic directorship of the Royal Danish Opera following proposed budget cuts, Hrůša announced that he would not take the music directorship of Royal Danish Opera, in solidarity with Warner's action.
[13] In March 2017, the Philharmonia Orchestra announced the appointment of Hrůša as one of its two new principal guest conductors, effective with the 2017–2018 season.