The Ottawa Senators first signed Beveridge, but he broke in as an NHL rookie on loan to the Detroit Cougars in 1929–1930. His season with Detroit was not successful and he was returned to the Senators after the season. He first received playing time for the Senators during the 1930–31 season, playing 8 games. The Senators were not a good team that year and his goals against average was 3.69. When Ottawa suspended operations for the 1931–32 season, Beveridge found himself in the minors with Providence. He led the Canadian-American league in wins that year. Ottawa resumed play in the NHL for 1932–33 and Beveridge was back with the Senators as backup to Alex Connell. After Alex Connell injured his knee in a December game against Chicago, Beveridge had a chance to play regularly. He got 3 shutouts in his first 8 games, but did not keep the job when Connell returned. When Connell struggled, Beveridge was able to play more. He played one more year for the Senators and went with the rest of the players to play in St. Louis for the Eagles. When the Eagles folded, the players were dispersed in a draft where he was picked up by the Montreal Canadiens. However, he never played for the Canadiens, being sold to the Maroons, again to substitute for Alex Connell when he retired. In 1935–36, the Maroons obtained Lorne Chabot from Chicago. Beveridge couldn't get back in the line-up after Chabot took over goaltending duties. However, Chabot retired after the season seemingly giving Beveridge another chance. In 1936–37, Alex Connell returned to the Maroons, and Beveridge was his back-up yet again. Connell struggled and then Beveridge replaced Connell for a third-time. This time Beveridge played well and the Maroons finished third in the Canadian Division, making the playoffs. They would go on to defeat the Boston Bruins in the playoffs. In the next series though the Rangers were led by former Maroon goalie Dave Kerr who shut them out twice. That would be the Maroons' final playoffs and Beveridge's only NHL playoff experience. He played for minor league teams until the 1942–43 season, when he received the call-up to the New York Rangers for a last hurrah. He played in 17 games, and recorded a shutout. After the season, he joined the Canadian Army. After his service, he finished his playing days playing senior league hockey for the Ottawa Commandos of the Quebec Senior League.
After hockey
After retiring from hockey for good in 1945, Beveridge became a coach at Carleton University. He also became a city councillor. As one of the last surviving Ottawa Senators, he was present at the opening game in 1992 for the new Senators. He lived to see Don Beaupre get the first shutout for a Senators goalie in 50 years during the 1994–95 season, before he died on February 13, 1995. He is interred in Beechwood Cemetery in Ottawa.
