Whilst in Gullane Primary School, Hunter-Hill first played mini rugby for North Berwick Rugby Club. His rugby talent was spotted while at Stewart's Melville College. He won the Brewin Dolphin Shield with Stewart's Melville.[2]
He later won a place to be coached in New Zealand in the summer of 2015 winning the prestigious John Macphail Scholarship.[3] He spent 15 weeks there.[4] He played for Stirling County, captaining the side, when not involved in Warriors duty.[5][6]
He was named as part of the new Glasgow district Rugby Academy founded by the Scottish Rugby Union in 2015.[7]
He made his debut for Glasgow Warriors coming off the bench in a friendly against the Army Rugby Union side in September 2015.[8] The Warriors won the match 71–0.
Hunter-Hill again turned out for the Warriors in the pre-season match against Harlequins on 20 August 2016.[9]
He made his competitive debut for the Warriors on 8 October 2016 when he replaced Rob McAlpine in the away match against Zebre in the Pro12.[10]
On 16 November 2016 it was announced that Hunter-Hill had joined London Scottish in a short-term loan move.[11]
On 15 May 2017 it was announced that he had secured a professional contract and signed for Edinburgh Rugby.[12]
On 13 September 2019 it was announced that he was joining Saracens on academy loan.[13] He has since signed a long term permanent contract to remain at Saracens until 2023.[14]
He helped Saracens win the Premiership title in 2023, featuring as a replacement in the final as Saracens defeated Sale Sharks.[15]
On the 28th June, 2024, it was announced Hunter-Hill had signed for the former Premiership champions of the previous season Northampton Saints.[16]
He re-signed for Edinburgh Rugby on 30 June 2025.[17]
He played for Scotland for the under-18s and captained the side.[18] He captained Scotland U20s.[19]
