Trapp made his debut on 1 August in the 2015 Trophée des Champions in Montreal, keeping a clean sheet in a 2–0 win over Lyon. He then kept four clean sheets in the first four league matches of the season. His five consecutive clean sheets ended when he conceded two goals, including a mistake that allowed Wahbi Khazri to capsulized the mistake, in a 2–2 draw against Bordeaux on 11 September 2015. Despite the mistakes, Trapp regained his first choice goalkeeper role and then made amends from his mistake against rivals, Marseille on 4 October 2015, making impressive saves, including saving a penalty from Abdelaziz Barrada, as PSG won 2–1. However, he suffered a hamstring injury while on international duty and missed one match as a result. Trapp returned to the starting line–up against Real Madrid in the UEFA Champions League match on 21 October 2015, starting the whole game, as he helped the side keep the match goalless, in a 0–0 draw. Trapp went on to earn a total of four clean sheets, as PSG advanced to the UEFA Champions League Group Stage. Following this, he kept three consecutive clean sheets between 19 December 2015 and 16 January 2016 against SM Caen, Bastia and Toulouse. Trapp then played in both legs of the UEFA Champions League Round of 16 against Chelsea, as he helped the side win 4–2 to advance to the next round. During the 2015–16 season, Trapp overtook Salvatore Sirigu as PSG's first choice goalkeeper in the club's Ligue 1 and UEFA Champions League matches, while the Italian played in the Coupe de France and Coupe de la Ligue, as he helped the club won a domestic quadruple. At the end of the 2015–16 season, Trapp went on to make forty–six appearances in all competitions.