In 2011, Péter Hornyák made his debut in Dunaferr Alexandra among adults in Nemzeti Bajnokság I. He then spent two seasons at Balatonfüredi KSE, where he was given more and more opportunities to play. At the age of 18, he was contracted abroad and certified for the German second division team of TUSEM Essen. Here he soon became the team's main man, and he was the team's number one penalty shooter.[1] They were also satisfied with his performance at the club, but after two seasons he was confirmed again to Hungary, the Csurgói KK, mainly due to his homesickness. In both of his seasons in Csurgói KK, he reached the third round of the EHF Cup qualifiers with his team. From the autumn of 2017 he became a player of Balatonfüredi KSE again. He spent two seasons with the Balaton shore team, and from the summer of 2019 he continued his career with Grundfos Tatabánya KC.[2] On September 25, 2021, he suffered a cruciate ligament rupture in the SBS-Eger-Grundfos Tatabánya KC match.