[2] He previously played with Senators teammates Jake Sanderson, Shane Pinto and Jacob Bernard-Docker at UND.

[4] An injury to Jakob Chychrun allowed Kleven to play in his first NHL game shortly after joining the team.

[12] For the 2024–25 season, Kleven made the Ottawa Senators out of training camp and was in the opening night roster.

[13] He scored his first NHL goal against Mackenzie Blackwood on November 27 in a 4–3 win against the San Jose Sharks.

[15][16] Following the end of the NHL season, Kleven joined the Team USA at the 2023 IIHF World Championship.