On 9th August 2020 Norwich announced that six Academy youngsters, including Hills had signed with the Club as first-year scholars with the Canaries. Bradley is described as a central defender.

He played for Norwich's first-team in their pre-season friendly with Hibernian in July 2022.

He was on the bench for Norwich's Championship clash with Burnley on 25th October 2022. He then signed a new contract on 10th November 2022 which will keep him at Carrow Road until 2025 with an option of a further year.

On 17th July 2023 he joined Accrington Stanley on a season-long loan. He said "I need to be tested. A loan this season is perfect. I'm buzzing to come over. I need to use this as a stepping stone to prove to the manager that I can play for Norwich one day."

Hills made his league debut as Accrington beat Newport 3-0 on the opening day of the 2023/24 season (5th August 2023) with Hills named as man of the match.