Hieronymus started his career with local side TuS Hamburg at the age of six and was a promising talent for the sweeper position when the then Hamburger SV general manager Günter Netzer snapped him up from local counterpart FC St. Pauli for DM 75,000 following Hamburger SV's Bundesliga title in 1979. The next Bundesliga season saw the technically gifted player playing his first games, being a starter in the European Cup final defeat of his side against Nottingham Forest at the Santiago Bernabéu Stadium on 28 May 1980. Failing to claim the Bundesliga trophy of 1980 and 1981, on both occasions Hamburg finished second, Hieronymus won his first trophy in 1982 when Hamburg won the league. That same summer he and his side crashed to Sven-Göran Eriksson's IFK Göteborg in the two-legged UEFA Cup final. In 1983 his club retained the Bundesliga title and, further, beat Juventus in the European Cup final in Athens. He was back as a regular in the line-ups of Hamburg manager Ernst Happel after his career had, for some time, been called to a halt due to his club signing veteran German legend Franz Beckenbauer in November 1980.