Galbraith played for Carnmoney Colts,
Ballyclare Comrades,
Glentoran,
Crusaders and
Linfield in his youth. In 2017, he left Linfield and joined the
youth academy of English club
Manchester United on a one-year scholarship, before signing a two-year professional contract with the club in May 2018. On 28 November 2019, he made his senior debut in a
UEFA Europa League match against Kazakh team
Astana, coming on as an 89th-minute substitute for
Tahith Chong. In October 2020, Galbraith signed a new three-year contract with United, with the option of an extra year.
Doncaster Rovers and Salford City loans He joined
League One club
Doncaster Rovers on a season-long loan in August 2021. On 26 October, Galbraith scored his first goal for Doncaster, scoring the equaliser in a 1–1 draw with
Cambridge United with a strike from 30 yards. Manager
Richie Wellens praised his performances, predicting that he would go on to have a long and successful career. Galbraith described his spell at Doncaster as a "great experience" despite the team being relegated. On 1 September 2022, Galbraith joined
League Two side
Salford City on a season-long loan, managed by former United youth coach
Neil Wood. He scored his first goal for the club on 8 October in a 1–0 win against
Northampton Town, Salford's first win against their opponents. On 16 May 2023, Galbraith confirmed that he will leave Manchester United at the end of 2022–23 season.
Leyton Orient On 29 June 2023, Galbraith signed for
Leyton Orient, rejoining former manager Richie Wellens.
Swansea City On 4 July 2025, Galbraith signed for
Swansea City for an undisclosed fee and on a three-year contract, with an option for an additional 12 months. He made his debut on 9 August 2025, starting in a 0–1 loss against
Middlesbrough. He scored his first goal for the club in a 3–1
EFL Cup first round win over
Crawley Town, scoring the third in
stoppage time via a volley from outside of the box. ==International career==