In the spring of 2011, Kovtun began training with Nikolai Morozov. He debuted on the ISU Junior Grand Prix (JGP) circuit in the 2011–12 season, winning gold at his first event in Romania and then silver in Estonia. He qualified for the 2011–12 JGP Final where he finished fourth. At the 2012 Russian Championships, Kovtun finished twelfth on the senior level and won the bronze medal on the junior level. He was assigned to the 2012 World Team Trophy—his first senior international event—following Sergei Voronov's injury-related withdrawal. He finished twelfth at the event.