Grimshaw signed for Argyle just after the start of the 2024/25 season, following Michael Cooper's departure to Sheffield United. 

Born in Salford, Grimshaw is a product of the Academy at Manchester City, the club he supported as a boy. Learning his trade alongside the likes of Ederson, Grimshaw played for City’s under-19s and development sides, as well as having loans out to Hemel Hempstead then Belgian side Lommel.   

In the summer of 2021, Grimshaw signed for Blackpool. Over two seasons, he battled for the number one jersey with Blackpool captain Chris Maxwell, and became the undisputed first choice in 2023/24, playing all but one league game, and keeping 18 clean sheets.