[8] On 21 May 2019, Kochetkov was traded by Sochi to contending club, SKA Saint Petersburg, in exchange for fellow goaltender Nikita Bogdanov.

After an assignment to SKA-Neva in the VHL, Kochetkov returned to SKA and having collected 3 wins in 6 games was traded to his third KHL club, HC Vityaz, along with Alexei Byvaltsev in exchange for Alexander Samonov and Artyom Shvets-Rogovoy on 18 October 2019.

In the following 2020–21 season, Kochetkov made two starts in four winless appearances with Vityaz, before he was assigned to VHL affiliate club and former team, HC Ryazan.

[13] He made his NHL debut on 23 April 2022, starting for the Hurricanes and earning two wins in two victories in a row over the New Jersey Devils and New York Islanders.

[15] On 3 March 2023, playing for the AHL's Chicago Wolves, Kochetkov scored a long-distance goal against the Manitoba Moose in Winnipeg.

[17] Earning the starting goaltender role, he collected 4 wins in 5 games, helping Russia claim the Bronze medal against Switzerland on 6 January 2019.