Brierley started playing junior football for local team Roach Dynamos in Heywood and after trials at the academies of Blackburn Rovers and Manchester City,
Brierley joined Rochdale's academy aged seven.[3] Brierley was named on Rochdale's bench for a FA Cup match against Newcastle United in January 2020, at the age of 15. Because of his age, Brierley had to get changed separately to the rest of Rochdale's first team.[6] He made his professional debut for Rochdale on 5 September 2020 in a 1–0 EFL Cup victory away to Huddersfield Town.[7] He signed his first professional contract with the club on 26 November 2020, having turned 17 earlier that week.[8] He made his league debut as a late substitute in a 2–0 defeat away to Ipswich Town on 26 September 2020, and made a further four league appearances across the 2020–21 season as Rochdale were relegated to EFL League Two after finishing 21st.[9][10]
Having made just three cup appearances for Rochdale during the 2021–22 season,[11] Brierley joined National League North side Spennymoor Town on loan for the remainder of the season on 24 March 2022.[12] On 29 April 2022, Brierley was recalled from this loan spell by parent club Rochdale,[13] and started Rochdale's final two matches of the season.[11] He was nominated for the LFE League Two Apprentice of the Season award, but lost out to Junior Tchamadeu of Colchester United.[14][15]
In July 2022, Brierley agreed an extension to his contract with Rochdale until summer 2024.[16] He scored his first senior goal for the club in a 3–3 EFL Trophy draw away to Accrington Stanley on 30 August 2022.[17] In January 2023, Brierley spent time on trial at both Sheffield United and Blackburn Rovers. Brierley was unable to sign for Sheffield United due to the club being under a transfer embargo, whilst a deadline day transfer to Blackburn fell through after the English Football League rejected their application to register the player. Blackburn appealed this decision unsuccessfully, and Brierley returned to first-team action for Rochdale in late February.[18][19][20] With Rochdale embroiled in a relegation battle, Brierley registered three assists in his first four games back as Dale picked up five points.[19] However, Rochdale were eventually relegated after finishing bottom on 38 points,[21] with Brierley having made 25 league appearances.[22]
On 2 June 2023, it was confirmed that Brierley had signed for Brentford for an undisclosed fee on a three-year deal.[23][24]
On 26 June 2025, Brentford announced the player had signed a one-year loan deal with Exeter.[25]