Professional
On April 12, 2014, Brown was signed as an undrafted free agent to a two-year entry-level contract with the Carolina Hurricanes. Brown was recalled to make the Hurricanes opening night roster in his first professional season in 2014–15. He made his NHL debut with the Hurricanes in a defeat to the New York Islanders on October 10, 2014. He recorded his first career NHL goal and assist on March 31, 2016, against the New York Rangers. He spent the majority of his tenure in the Hurricanes' organization with their American Hockey League (AHL) affiliate, the Charlotte Checkers, where he was team captain from 2016 to 2019 and won a Calder Cup in 2019.
After spending the first five seasons of his professional career within the Hurricanes organization, Brown left as a free agent to sign a two-year, $1,400,000 contract with the Vegas Golden Knights on July 1, 2019. He spent most of the season with the Golden Knights' AHL affiliate, the Chicago Wolves. He appeared in one regular season game in his first year with Vegas, scoring against the Anaheim Ducks on February 23, 2020. At the end of the season he spent time on the team's taxi squad and was put into the team for Game 3 of the first round series against the Chicago Blackhawks after Paul Stastny and Tomáš Nosek were unable to play. He scored his first NHL playoff goal in that game in a 2–1 victory. The Golden Knights eliminated the Blackhawks and advanced all the way to the Western Conference Final where they were defeated by the Dallas Stars. He finished the playoffs with 12 games played while scoring two goals. In 2021, he was named the team captain of the Golden Knights' new AHL affiliate, the Henderson Silver Knights.
Brown was placed on waivers by the Golden Knights on October 10, 2021 and claimed by the Philadelphia Flyers the next day. Brown was limited to 44 games in his first year with Philadelphia, suffering a pair of injuries. He played mainly on the fourth line as a faceoff specialist. On January 11, 2023, Brown played in his 100th NHL game.
On March 3, 2023, the Flyers traded Brown to the Ottawa Senators in exchange for a sixth-round pick in the 2023 NHL entry draft. The Senators acquired Brown as depth for the center position. He finished with 43 games for the Flyers during the 2022–23 season, registering two goals and seven points. Following the end of the season, Brown joined Team USA at the 2023 IIHF World Championship. The team finished fourth in the tournament.
As a free agent from the Senators, Brown was signed to a two-year, $1.6 million contract to join his fifth NHL club, the Boston Bruins on July 1, 2023. At the end of the 2023 training camp, Brown failed to make the Bruins roster and was waived on October 8. Brown went unclaimed and was assigned to Boston's AHL affiliate, the Providence Bruins, on October 9. However, his stay in Providence was brief as he was recalled by Boston on October 10. He was returned to Providence on November 25 after appearing in eight games with Boston, registering one point. Afterwards, Brown spent most of the rest of his season in Providence, having two brief call ups to the NHL squad in late December and January which totaled three games. On May 5, 2024, Brown was called back up to the NHL ahead of the Bruins second round Stanley Cup playoffs series against the Florida Panthers. He played Game 1 of the series, replacing Jesper Boqvist, in what was his first NHL game since January 27. The Bruins were eliminated by the Panthers in six games.
In his second season with the Bruins, he went unclaimed on waivers and assigned to Providence to start the 2024–25 season. He was named the 27th captain of Providence on October 17, 2024.
Having spent the first 12 seasons of his professional career in North America, Brown left the Bruins as a pending free agent and signed his first contract abroad in agreeing to a one-year deal with German club, Adler Mannheim of the DEL, on June 12, 2026.
