Born in
Salford, Grimshaw joined his local club
Manchester City as a teenager. In June 2018, he signed a new three-year deal with the club. He was involved in a matchday squad for Manchester City for the first time in January 2019 as an unused substitute in an
EFL Cup tie with
Burton Albion. In January 2020, he joined
National League South side
Hemel Hempstead Town on loan until the end of the season. On 5 October 2020, he joined
Belgian First Division B side
Lommel on a season-long loan deal.
Blackpool Grimshaw joined
Blackpool on 1 July 2021 after signing a two-year contract, with the club having the option to extend it for a further twelve months. He joined them on a free transfer as his Manchester City contract had expired. After an injury to Blackpool's captain
Chris Maxwell on 2 October 2021, Grimshaw deputised for nine games. Maxwell returned on 4 December, but was again injured at
Derby County the following week. Grimshaw returned to the starting line-up in Blackpool's 3–1 victory over
Peterborough United on 18 December. On 4 July 2022, Grimshaw signed a three-year extension to his contract plus an option for a fourth year.
Plymouth Argyle On 23 August 2024, Grimshaw signed for Championship club
Plymouth Argyle for an undisclosed fee.
Norwich City On 6 June 2025, Grimshaw returned to the Championship following Argyle's relegation, joining
Norwich City on a three-year contract for an undisclosed fee. ==Career statistics==