Syme became a first year Academy scholar at Norwich City in July
2015. He plays as a full-back.
On 5th May 2017, it was announced that Syme would be leaving the Canaries when his contract expired at the end of June 2017.
In July 2017, he trialled with Bolton Wanderers playing for their Under-23s at Atherton Colls. He subsequently signed for Hitchin Town. He made 28 appearances for Hitchin in 2017/18 scoring once.
In July 2018 he moved to Kings Langley but in the October of that year he joined Leverstock. In July 2019 he moved to Tring Athletic before moving to Harpenden Town in January 2020.