Gore gia nhập học viện Manchester United vào năm 2018, trước đó từng chơi tại Burnley. Anh ấy đã vô địch 2022 FA Youth Cup cùng Manchester United. Anh ấy được bầu chọn là Cầu thủ của năm của đội dự bị của Manchester United cho Mùa giải 2022–23.[2]

In August 2023, as well as featuring for the club in the EFL Trophy, he was included in the Manchester United first team squad and on 26 August 2023 for the first time was named as a substitute in the Premier League match against Nottingham Forest.[3][4] In September 2023, he was named as part of the match day squad in the UEFA Champions League against Bayern Munich. On 26 September 2023, he made his senior debut for Manchester United against Crystal Palace in the EFL Cup as a replacement for Sofyan Amrabat, largely impressing with his work rate and pace.[5]