Quispel started playing football at the age of six at WKE '16. He later went to VV Emmen. From there, he went to FC Twente and played there for four years. In 2015, he joined FC Emmen.[1] Quispel made his professional debut with FC Emmen in a 2–0 Eredivisie loss to SC Heerenveen on 17 August 2019.[2]
In the summer of 2020, he went to play for German Regionalliga side VfB Oldenburg, which signed him free of charge.[3] A few months later, he left there again to join the PEC Zwolle's reserve team on an amateur basis, where his younger brother Jan also was playing.[4]
In July 2021, Quispel switched to Derde Divisie club ACV.[5] In January 2022 it was confirmed that from the upcoming 2022–23 season Quispel would play for league rivals VV Staphorst.[6] In February 2023, ACV confirmed that Quispel would return to the club ahead of the 2023–24 season. ACV was promoted to the 2023–24 Tweede Divisie prior to Quispel's return.[7]
On 22 June 2024, Quispel returned to Emmen on a two-year contract.[8]
Personal life
Quispel's father, Joost Quispel, was also a footballer who played for FC Emmen.[9]