Eyssimont landed with his fifth NHL team when he signed a two-year, $2.9 million contract with the Boston Bruins on July 1, 2025. He was acquired by the Seattle Kraken in a three-team trade with the Tampa Bay Lightning and Detroit Red Wings on March 5, 2025.

He signed a two-year, $1.6 million contract with the Lightning on May 5, 2023, after he was acquired from the San Jose Sharks on March 1, 2023, and had a goal and assist in 15 regular-season games. He made his Stanley Cup Playoff debut in Game 1 of the 2023 Eastern Conference First Round and had a goal and assist in Game 5.

The forward had five points (one goal, four assists) in 19 games for the Winnipeg Jets before he was claimed off waivers by the Sharks on Jan. 6, 2023. He had eight points (three goals, five assists) in 20 games with the Sharks. The fifth-round pick (No. 142) of the Los Angeles Kings in the 2016 NHL Draft made his NHL debut with Winnipeg on April 11, 2022. He signed a two-year, two-way contract with the Jets on July 28, 2021, and played for Manitoba of the American Hockey League until he was promoted to the NHL on April 11.

Eyssimont signed his first pro contract, a two-year, entry-level deal, with the Kings on March 29, 2018, after playing 39 games in his junior season for St. Cloud State University. He helped St. Cloud to the best regular-season record in the NCHC and No. 1 seed in the NCAA Tournament, where they lost to Air Force in the West Regional Semifinal. Eyssimont led the Huskies in goals (17), was second in points (39) and third in assists (22). His collegiate career ended with 101 points (45 goals, 56 assists) in 115 games.

Prior to attending St. Cloud State, Eyssimont played for Fargo and Sioux Falls of the United States Hockey League. He helped Sioux Falls win the 2015 Clark Cup with 16 points (seven goals, nine assists) in 19 playoff games that tied for the team lead.