Murray ultimately joined the Fargo Force of the United States Hockey League (USHL) for his final junior season.

After the conclusion of his time in juniors, Murray played five seasons of collegiate hockey with the University of Massachusetts Amherst.

[3] On October 31, 2022, Murray was signed to a one-year entry-level contract by the Dallas Stars of the National Hockey League (NHL), Texas' major-league affiliate.

[4] Shortly afterwards, he was recalled to Dallas' main roster as the result of an injury to starting goaltender Jake Oettinger, with Murray serving as backup to Scott Wedgewood.

[10] Murray appeared for the Canada West team in four games at the 2015 World Junior A Challenge, posting a .911 save percentage and 2.75 goals against average en route to a gold medal.