In 2013 Walker signed with the Youngstown Phantoms of the junior United States Hockey League, moving to North America for the first time.

He attended the training camp of the Washington Capitals in 2013 and signed with their AHL affiliate Hershey.

Walker began playing hockey at age six and by thirteen he was in a league with players as old as twenty and able to outplay them.

[1] As a result of his play in the Extraliga, Walker began to be noticed by the National Hockey League (NHL).

[14] Upon the conclusion of the season Walker returned to the Czech Republic to train, before heading back to Australia.

[16][17] However, due to an overlooked rule, the Capitals were unable to sign Walker; as he had started the 2012–13 season in Europe and then moved to North America, and was under 20 years old, he would have to enter the 2014 NHL Entry Draft before being allowed to sign an NHL contract.

[18] Instead, on 24 September Walker signed a contract with the Capitals' American Hockey League affiliate, the Hershey Bears.

[20] During Walker's third game with the Bears, on October 27 against the Norfolk Admirals, he scored his first goal and recorded his first professional fight.

[28] He played 58 games for Hershey in 2016–17, recording 23 points and was re-signed by the Capitals to a two-year contract after the season finished.

[37] After six seasons within the Capitals organization, Walker left as a free agent to sign on a one-year, two-way contract with the St. Louis Blues on 1 July 2019.

[38] Walker again spent most of the season in the AHL (this time with the San Antonio Rampage), but also played in five NHL games, scoring his first goal as a Blue on 30 November against the Pittsburgh Penguins[39] and an assist against the Chicago Blackhawks three days later.

[41] On 9 December 2021, Walker scored his first NHL hat trick in a 6–2 Blues victory over the Detroit Red Wings.

Welsh born Walker first played for the Australian men's senior team at the 2011 IIHF World Championship Division II Group A tournament which was held in Melbourne, Australia.

[46] Walker was born in Cardiff, Wales to Wayne and Ceri; he also has an older brother, Ryan.

[47] When Walker was two, his family moved to Sydney, Australia where he started at Kirrawee High School.

[48] Ryan, his older brother, also played hockey representing Australia in the national under-18 squad.