Kostin debuted for HC MVD in the Junior Hockey League (MHL) during the 2015–16 season. In 30 games for the team he scored 8 goals and 13 assists.
Kostin was selected first overall in the 2016 CHL Import Draft by the Kootenay Ice of the Western Hockey League (WHL), a major junior league in Canada, but he decided to stay in Russia with Dynamo Moscow for the 2016–17 season.He was reluctant to play on a junior team in North America, instead preferring to play for a senior team, either in the NHL or American Hockey League (AHL), the top minor league affiliate for the NHL.
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