Playing on the top line with Sam Reinhart and Connor McDavid, Klimchuk scored eight points to help lead Canada to a gold medal at the 2013 IIHF World U18 Championships.

He credited the chance to play in all offensive and defensive situations with helping him develop a strong two-way game.

[13] During the 2018–19 season, on November 27, 2018, Klimchuk was traded by the Flames to the Toronto Maple Leafs in exchange for Andrew Nielsen.

[14] Klimchuk appeared in just 13 games with the Toronto Marlies, before he was traded by the Maple Leafs for the second time within the season to the Ottawa Senators in exchange for Gabriel Gagne on January 11, 2019.

[15] He finished the season with Ottawa's AHL affiliate, the Belleville Senators scoring four goals and five points in eight games before a season-ending shoulder injury.