Growing up in Maltby, a small former mining town in South Yorkshire, Kirk first got into hockey when his parents and family went to watch the Sheffield Steelers. His brother Jonathan got into ice hockey and Kirk wanted to be like his brother, so he also started playing. Kirk began playing for the Sheffield Junior Academy. He was selected for the Midlands Conference – a team consisting of the best players from the Midlands region of the UK at U11, U13, U15 and U17 level – every year of eligibility, winning the EIHA Conference Tournament twice and being named a tournament all-star six times out of a possible eight, as well as being named tournament MVP three times. Playing in the England U18 North League in the 2015–16 season, Kirk amassed a league-leading 98 points, with 60 goals and 38 assists. The same year, the U18 team from Sheffield won the league title. He was also selected for the Great Britain U16s. Continuing his success as an U18, Kirk played in the EPL for the Sheffield Steeldogs and was signed by the Sheffield Steelers on a three-year apprentice contract. Kirk has represented Great Britain at all age groups. In the 2017–18 season, he played for the U18s, coming away with a gold medal. For the U20s, he collected a range of awards such as Best Forward, Most Points, Most Assists, Most Goals, as well as the Best Face-off Percentage and a bronze medal. Although he didn't get any points, he represented the Great Britain men's team in the Division 1A World Championships. Great Britain won the tournament and were promoted to the top tier of world ice hockey. They now compete against the leading hockey nations such as Canada, USA, Finland, Russia and Sweden.
North America
Kirk was selected 189th overall in the 2018 NHL Entry Draft by the Arizona Coyotes. He became the first player born and trained in England to be drafted into the NHL. Kirk was selected 8th overall in the CHL Import Draft later in June and currently plays for the Peterborough Petes of the Ontario Hockey League.
International play
Kirk has played for the British national team in several international tournaments at both the junior and senior level. His senior debut came at the 2018 IIHF World Championship Division I, where he helped Great Britain earn promotion to the 2019 World Championship. It marks Great Britain's first appearance at the elite division since 1994. Kirk played five games, though he did not score a point.