He scored his first AHL playoff goal in Game 5 of their first-round series against the Pirates to help the Monarchs advance to the Eastern Conference semifinals.

[8] Kempe then scored goals in Games 3 and 4 of the Eastern Conference Finals to help the Monarchs sweep the Hartford Wolf Pack.

[13][notes 1] Due to injuries throughout the lineup, Kempe spent the majority of the season playing centre as opposed to his typical winger position.

[15] Kempe began the season scoring one goal over eight games before recording his first AHL hat-trick on 5 November to lead the team 4–1 over the San Diego Gulls.

[16] He missed some time in December to compete with Team Sweden at the 2016 World Junior Ice Hockey Championships.

[1] When attending the Kings 2017 training camp, Kempe was put on a line with Justin Auger and Kyle Clifford.

[30] An injury to Jeff Carter in late October resulted in Kempe moving onto the Kings second line with Tyler Toffoli and Tanner Pearson.

[32] While playing with Toffoli and Pearson, Kempe scored 14 goals through his first 44 games but was bumped back to the third-line once Carter recovered from his injury.

[35] Kempe returned to the Kings lineup for the 2018–19 season,[36] where he was expected to play as a winger on their second line with Ilya Kovalchuk and Jeff Carter.

[37] Due to injuries throughout the lineup, Kempe began playing alongside rookies Matt Luff and Austin Wagner on the Kings third line.

[46] He was made a healthy scratch for a November game against the Minnesota Wild[47] before returning to the lineup as a left winger instead of center.

[48] When the NHL paused play due to the COVID-19 pandemic, Kempe led the team with four shorthanded points while averaging 16:01 of ice time per game.

[54] Entering his sixth season with the Kings, 2021–22 would be a breakout year for Kempe, who posted new career highs scoring 35 goals and 54 points.

He would also participate in his first NHL All-Star Game, held in Las Vegas; he is the only player from the Kings named to the All Stars this season.

[59] Kempe's older brother Mario also played professional ice hockey, including 52 games with the Arizona Coyotes.