Quinn was born in New Zealand and played for Auckland, making his List A cricket debut in February 2013 in the 2012–13 Ford Trophy.[2] At the end of 2015, he signed a three-year contract with Essex County Cricket Club. Quinn has a British passport so is not regarded as an overseas player.[3][4] On 5 May 2021, Quinn joined Kent County Cricket Club on loan for their next four matches in the 2021 County Championship.[5] On 16 June 2021, Quinn signed a three-year contract with Kent to start from 2022 and also rejoined on loan for the remainder of the 2021 season.[6] He signed a one-year contract extension with the club in October 2024.[7]