A member of the club's under-20 squad, King was predominantly a midfielder, however could also play right back and centre back. Having yet to feature for the first teamin September 2013, with the transfer window coming to a close, Premier League outfit Swansea City made an offer believed to be a five-figure sum of money for King. However, Hearts administrators BDO rejected the offer. Having been included in the match day squad for every game so far that season, yet not featured, he made his first team debut for Heart of Midlothian as a substitute in a friendly against German Bundesliga side Wolfsburg on 13 November 2013. He made his full professional debut in a Scottish Cup tie against Celtic on 1 December 2013, coming on as a substitute in the 79th minute replacing Jamie Hamill. He went on to make his first Scottish Premiership appearance on 21 December, playing from the start against Celtic at Celtic Park. In January, Swansea renewed their interest in King and a further bid was accepted by the club. In all he made three appearances for Hearts. He has featured at both under-18 and under-19 levels for Scotland. King was nominated by STV Sport as one of 14 young players in Scottish football to watch in 2014.
Swansea City
On 28 January 2014, King joined Premier League side Swansea City on a three-and-a-half-year deal, for an undisclosed fee. He initially joined up with the club's under-21 squad. On 3 January 2015, King made his Swansea City debut in a 6–2 FA Cup win over Tranmere Rovers. In May 2015, King won the 2014–15 Professional U21 Development League 2 title as part of the Swansea Under-21 team. In July 2015, King joined League One team Crewe Alexandraon loan until 6 January 2016. King returned to Swansea on 5 January 2016. On 5 August of the same year he signed a season-long loan deal with League One side Southend United, but this was cut short in January 2017, with the player returning to Swansea City. On 29 January 2018 King signed on loan for League Two side Mansfield Town for the rest of the season. On 2 July 2018, he joined Peterborough United on another loan deal set to last until January 2019, but he returned to Swansea City the following month after his loan was terminated because of injury.
Dundee United
King left Swansea to join Scottish Championship club Dundee United on a three-year contract in July 2019. His brother Billy had left United the previous season.