The Los Angeles Kings selected Prokhorkin, a forward from Chelyabinsk, Russia, in the fourth round (No. 121) of the 2012 NHL Draft. But his path to the NHL was a long one.

The Kings signed Prokhorkin and assigned him to Manchester of the American Hockey League at the start of the 2012-13 season. But after eight games, he returned to Russia and played seven seasons in the Kontinental Hockey League. He helped SKA St. Petersburg win the Gagarin Cup in 2017 and was a member of the gold medal-winning Olympic Athletes from Russia team at the 2018 PyeongChang Olympics.

After helping SKA St. Petersburg reach the Western Conference final in the 2019 Gagarin Cup playoffs, Prokhorkin signed with the Kings on May 13, 2019.

Prokhorkin began the 2019-20 season with Ontario of the AHL, but was called up by the Kings and made his NHL debut at the Chicago Blackhawks on Oct. 27, 2019. He earned his first NHL point when he scored a goal against the Vegas Golden Knights on Nov. 16, 2019, and had his first multipoint game with two assists at the San Jose Sharks on Dec. 27, 2019.