1 European skater by NHL Central Scouting, stating he has proved in earlier viewings that he has the necessary tools to excel at the next level.

[3] Through playing a limited number of games, Kostin was taken with the last pick in the first round of the 2017 NHL entry draft by the St. Louis Blues.

Initially thought to continue developing in Russia, Kostin was made a free agent after Dynamo Moscow were forced to release all of their players through a violation of KHL rules on 4 July 2017.

[5] Kostin scored his first career NHL goal with the St. Louis Blues during the 2019–20 season on 23 November 2019, in a 4–2 loss to the Nashville Predators.

[6] Approaching the 2022–23 season, his sixth year within the Blues organization, Kostin was unable to clinch a role on the opening night roster and was placed on waivers before he was re-assigned to AHL affiliate, the Springfield Thunderbirds.

[8] On 29 June 2023, Kostin as a pending restricted free agent was traded to the Detroit Red Wings, along with Kailer Yamamoto, in exchange for future considerations.

[12] Kostin made his international debut at the 2016 IIHF World U18 Championships, serving as captain of the Russian U-18 team.