He started his career as a youth player at Rangers and was associated with the Ibrox club for six years until he was released, with the club saying he was "too small and too slight." He then signed for Kilmarnock in July 2014, and captained their under-17 and under-20 youth teams before making his progression into first team football in 2016.
Kilmarnock
Taylor made his first team debut for Kilmarnock on 14 May 2016, starting at left back in a Scottish Premiership game against Dundee United. He then made his second start in the second leg of the Scottish Premiership Play-off Final, which Kilmarnock won 4–0 against Falkirk to win the tie 4–1 on aggregate. After the 2015–16 season ended, Taylor signed a three-year contract with Kilmarnock. Having kept his place in the team under managers Lee Clark, Lee McCulloch and Steve Clarke, Taylor was rewarded with another new contract in April 2018, running until June 2021. Taylor scored his first goal for the club, the first in a 5-0 win against Hamilton Accies on 30 March 2019. During the summer 2019 transfer window, Kilmarnock rejected offers for Taylor from Nuremberg, Sunderland and Celtic.
Celtic
Taylor signed a four-year contract with Celtic on 2 September 2019.
International career
In March 2017, Taylor played in his first match for the Scotland under-21 side in a friendly against Estonia. Taylor was selected for the Scotland under-20 squad in the 2017 Toulon Tournament. In the team's second match in the tournament, Taylor scored the only goal in a 1–0 win against Brazil under-20. Taylor was also the only Scottish player named in the 'team of the tournament' as well as being named 4th best player. Taylor was named in the full Scotland squad for UEFA Euro 2020 qualifying fixtures in June 2019; he remained on the bench in the home game against Cyprus at Hampden Park. After captain Andy Robertson picked up an injury, Taylor debuted at left-back against the world's top-ranked team, Belgium on 11 June, and played the full match in Brussels as Scotland lost 3–0. Manager Steve Clarke hailed Taylor's debut as "excellent". He then played in the next two games, on 16 and 19 November, winning against Kazakhstan and Cyprus. His performances were praised especially for his link up play with left sided Celtic team mate, James Forrest.