Kovtun started the 2015–16 season with gold at the 2015 CS Mordovian Ornament. Turning to the Grand Prix series, he placed second in the short program (SP) at the 2015 Trophée Éric Bompard. Due to the November 2015 Paris attacks, the free skate was cancelled and the SP standings were deemed the final results. Kovtun finished tenth at his second GP event, the 2015 NHK Trophy, which meant he did not qualify for the Final. In December, he won his third consecutive national title, at the 2016 Russian Championships in his home city of Yekaterinburg.