Klünter broke into Köln's senior team during the 2016–17 season. In May 2017, he scored his first professional goal for Köln in a 2–2 draw with Bayer Leverkusen.[3] After the team's relegation following the 2017–18 season it was announced that Klünter would transfer to Hertha BSC in the summer.[4] He played for both the first team and the reserve team during the 2018–19 season.[5]