[12] Addison was selected by the Pittsburgh Penguins of the National Hockey League in the second round, 53rd overall, in the 2018 NHL entry draft.
[13] After his junior team was eliminated in the 2019 WHL playoffs, Addison joined Pittsburgh's American Hockey League (AHL) affiliate, the Wilkes-Barre/Scranton Penguins on an amateur tryout contract on April 19, 2019.
He was recalled due to a shortage of available defencemen for Minnesota and made his NHL debut on February 16, 2021, in the Wild's 4–0 loss to the Los Angeles Kings.
Addison made his NHL playoff debut on May 24, replacing the injured Carson Soucy, registering an assist on Jordan Greenway's goal in the first period of the Game 5 victory.
[22] In the next game on November 2, 2021, he scored his first NHL goal against goaltender Filip Gustavsson in a 5–4 overtime win against the Ottawa Senators.
[28] However, towards the end of the season, he struggled and was a healthy scratch for many games, especially after the Wild acquired defenceman John Klingberg at the trade deadline.
[30] He once again made the opening night roster for the Wild in the 2023–24 season but was passed on the team's depth chart by Dakota Mermis and Daemon Hunt.
On November 8, 2023, Addison was traded to the San Jose Sharks in exchange for Adam Raška and a 2026 fifth-round pick.
[7] After a lone season with the Sharks, Addison was not tendered a qualifying offer and left as an unrestricted free agent.
[34] After going un-signed over the summer, Addison accepted an invitation to attend the Ottawa Senators training camp for the 2024–25 season on a professional tryout (PTO) on September 6, 2024.
[35] After being released from his PTO, Addison joined the AHL Henderson Silver Knights on a one-year contract on October 24.