In August 2020, he signed for Leeds United ahead of their Premier League return and in 2021, represented Germany at UEFA Euro 2020.

FC Kaiserslautern's academy at the age of five, but switched to SV Dörbach when his family moved to Salmtal.

[6] He joined Eintracht Trier's academy in 2009,[7] and despite the fact that "he was never seen as a superstar talent" according to his childhood best friend, he was invited to regional trials by the German Football Association in 2011.

[5] He scored his first senior goal on 22 November 2014 in a 4–2 victory over SpVgg Neckarelz; A low shot in the 25th minute to put Eintracht Trier 1–0 up.

[14][15] He made 24 appearances for Kaiserslautern during the 2016–17 season,[16] and attracted the interest of multiple Bundesliga clubs according to his father Harry.

[19] On 29 August 2020, Koch joined newly-promoted Premier League club Leeds United on a four-year deal,[20][21] for a transfer fee that was reported to be £13 million.

[8] Koch made his Premier League debut for Leeds in the first match of the season against Liverpool on 12 September 2020, starting in the 3–4 defeat at Anfield to the reigning champions.

[27] Following the appointment of Jesse Marsch as manager at Leeds, and a switch to zonal marking,[28] Koch appeared to take a step up in his game and became a regular starter in central defence towards the end of the 2021–22 season and into 2022–23.

[36] Koch was called up to the Germany squad on 26 August 2020 for the UEFA Nations League fixtures against Spain and Switzerland.