After being an unused substitute in the first two matches, Compper made his RB Leipzig debut on 22 August 2014, where he came on as a substitute for injured Niklas Hoheneder, in a 1–0 win over Erzgebirge Aue. Since making his debut, Compper started every match for the side, alongside Tim Sebastain and Lukas Klostermann in the central–defence position. This lasted until Compper was suspended for a yellow bookable offence in February 2015. After returning, Compper was given the captaincy for a match against FSV Frankfurt on 15 February 2015, which they lost 1–0. His return was short–lived when he was sent–off in the first half, in a 0–0 draw against Karlsruher SC on 9 March 2015, resulting in him serving a two match ban. Despite being on the sidelines later in the 2014–15 season, Compper finished his first season, making a total of 27 appearances in all competitions.