Walker was born in Cardiff, Wales, but grew up in Australia and became the first Australian player drafted by an NHL team when he was selected by the Washington Capitals in the third round (No. 89) of the 2014 NHL Draft.
Walker moved to the Czech Republic in 2007 after dominating local competition in Australia. After six years in the Czech Republic, he signed with Youngstown of the United States Hockey League in January 2013 and finished with 27 points (seven goals, 20 assists) in 29 games. He spent most of the next four seasons with Hershey of the American Hockey League before making the Capitals at training camp in 2017.