Career
Before playing in the NHL, Copley played one season with the Tri-City Storm and one season with the Des Moines Buccaneers of the United States Hockey League (USHL). He also played two years with the Michigan Tech Huskies of the Western Collegiate Hockey Association (WCHA).
He was not drafted by an NHL team. On March 20, 2014, Copley signed a two-year, $1.41 million entry-level contract to join the Washington Capitals of the National Hockey League (NHL). He was sent down to play for their AHL-affiliate Hershey Bears where he played 20 regular season games.
On July 2, 2015, the Capitals traded Copley along with Troy Brouwer and a 2016 third-round pick to the St. Louis Blues in exchange for T. J. Oshie. They sent him down to play for their AHL-affiliate Chicago Wolves. On February 27, 2016, the Blues called him up and Copley made his NHL debut, coming in for relief of Jake Allen and stopping 5 of 6 shots in a 5–0 loss against the Nashville Predators.
On February 27, 2017, the Blues traded Copley along with Kevin Shattenkirk back to the Washington Capitals in exchange for Brad Malone, Zach Sanford, a 2017 first-round draft pick and a 2019 conditional second-round draft pick. On June 28, 2017, Copley signed a one-year, $1.3 million contract to stay with the Capitals. They sent him down to play for their AHL-affiliate Hershey Bears. On October 27, 2018, Copley stopped 27 of 30 shots for his first NHL career victory in a 4–3 shootout win against the Calgary Flames. On December 22, 2018, Copley stopped all 35 shots he faced to earn his first NHL career shutout in a 4–0 win against the Ottawa Senators.
On July 13, 2022, Copley signed a one-year, $850,000 contract to join the Los Angeles Kings. On October 1, 2025, the Kings placed Copley onto waivers and his contract was picked up by the Tampa Bay Lightning the next day. He never played a game for the Lightning. On October 15, 2025, the Lightning traded Copley back to the Kings for future considerations.
