Kostin, 23, split time between the Blues and the AHL's Springfield Thunderbirds during the 2021-22 season.
In 40 games in the NHL, Kostin recorded four goals and five assists (nine points). In Springfield, Kostin posted three goals and three assists in 17 regular-season games and eight points (four goals, four assists) in 18 Calder Cup Playoff games.
Kostin was drafted by the Blues in the first round (No. 31 overall) in the 2017 NHL Draft.