During his tenure in the OHL, Dunn began to gain attention from scouts and earned the IceDogs Top Defenceman of the Year Award in two consecutive seasons.

[4] In honour of Dunn's grandfather who was important in his development as a player, the family started a Canadian Tire Jumpstart memorial fund in his name.

[12] Dunn continued to improve in his second season with Niagara, totaling 56 points in 68 games[1] to clinch the team's Top Defenceman of the Year Award.

"[17] Dunn and the IceDogs qualified for the 2015 OHL playoffs, where he scored four goals in Game 1 against the Ottawa 67s to help the team win the series 4–2.

[15] He began the second round against the Oshawa Generals leading all defencemen before being suspended two games for slew footing Mitchell Vande Sompel.

[22] Dunn attended the St. Louis Blues 2015 Development Camp before returning for his final season of major junior hockey with the IceDogs.

[30] He made his NHL debut with the Blues against the defending Stanley Cup champions, the Pittsburgh Penguins, while playing a third pairing role in a 5–4 overtime win on October 4, 2017.

[34] At the conclusion of his sophomore season, Dunn was named to Canada's senior team to compete at the 2018 IIHF World Championship,[35] but was replaced by Josh Bailey due to an injury.

[38] In March 2019, Dunn recorded a new career-high in points with 27[39] and joined Alex Pietrangelo and Colton Parayko as the first three Blues defencemen to reach 10 goals in the same season.

[44] During the NHL's pause in play due to the COVID-19 pandemic, Dunn competed in a league-wide Fortnite tournament for charity with teammates Robert Thomas and Jordan Kyrou.

[45] Once the NHL returned to play, Dunn and the Blues loss to the Vancouver Canucks in the Western Conference First Round of the 2020 Stanley Cup playoffs.

[47] After five seasons within the Blues organization, Dunn's tenure ended on July 21, 2021, after he was the team's selection at the 2021 NHL Expansion Draft by the Seattle Kraken.

[51] Upon returning to the lineup, he scored the first goal in the history of Climate Pledge Arena for the Kraken in the first period of a 4–2 loss to the Vancouver Canucks.

[52] As the Kraken continued to lose games through November, head coach Dave Hakstol placed Dunn on a pairing with Adam Larsson.

[54] Dunn had a breakout season in 2022-23, setting career highs with 14 goals and 64 points, continuing his successful partnership with Larsson on the Kraken's top pair.

The Kraken also improved dramatically from the previous season, making the playoffs for the first time and defeating the Colorado Avalanche, the reigning Stanley Cup champions, in seven games before falling to the Dallas Stars in the next round.