Kivihalme, 23, spent the 2018-19 season with Karpat of Finland's Liiga. In 60 games during the 2018-19 season, Kivihalme recorded nine goals and 21 assists for 30 points, which ranked ninth among Liiga defencemen in scoring. He added nine points (4 goals, 5 assists) in 16 playoff games, which was the third highest point total among Liiga defencemen in the postseason. In Champions League play during 2018-19, Kivihalme recorded five points (2-3-5) in 10 games. Over two Liiga seasons, Kivihalme recorded 50 points (13 goals, 37 assists) in 104 career games, while adding nine points (4 goals, 5 assists) in 34 playoff games, capturing the Liiga championship in 2017-18 and collecting a silver medal in 2018-19.

Kivihalme was originally selected by the Nashville Predators in the fifth round (140th overall) of the 2013 NHL Draft. Prior to joining Karpat, he played at Colorado College (NCAA) for three seasons, recording 36 points (10 goals, 26 assists) in 107 career NCAA games.