Nagy started his career in Felcsút FC and then in 2011 he was signed by the partner team of Felcsút, Videoton FC. However, he could not earn any appearances during his two year at Videoton. Therefore, he was loaned to Nemzeti Bajnokság II club Puskás Akadémia of Felcsút, where he could play eight matches in the 2012–13 Nemzeti Bajnokság II season. His short spell convinced the owner of the club and he was purchased in 2013.
He debuted in the Nemzeti Bajnokság I in 2013, when Puskás Akadémia was promoted to the first division.
Since Zsolt Hornyák's appointment as the manager of Puskás Akadémia, he has become a stable member of the squad earning 25, 27, and 28 caps in the 2019–20, 2020–21, and 2021–22 seasons, respectively.
Nagy made his debut for Hungary national team on 15 November 2019 in a friendly against Uruguay. He substituted Mihály Korhut in the 75th minute.[3]
On 11 June 2022, he scored his first goal against Germany in the 2022–23 UEFA Nations League A match at the Puskás Aréna. The match ended with a 1–1 draw.[4] Three days later, he scored Hungary's third goal in their 4–0 win over England in the same competition.[5]
On 14 May 2024, Nagy was named in Hungary's squad for UEFA Euro 2024.[6] He appeared as a substitute for Milos Kerkez in both the 2–0 loss to Germany[7] and the 1–0 win over Scotland as the Magyars finished third in Group A.[7]