Bevan played in his native New Zealand with Western Springs before moving to Auckland City, where he made his first-team debut on 28 February 2016, as an 86-minute substitute against WaiBOP United.[1] In the summer of 2016, Bevan moved to the Nike Academy in England.[2]
In 2018, Bevan moved to Sweden's third-tier on loan at Husqvarna FF.[5] After making five starts, he returned to his parent club. Later that season, he went on loan in the USL with the Whitecaps' affiliate club, Fresno FC.[6]
Bevan joined Auckland City in 2021 after being released by TS Galaxy.[11]
Cavalry FC
On 28 January 2022, Bevan returned to Canada, signing with Canadian Premier League side Cavalry FC.[11] He scored his first goal for Cavalry in the preliminary round of the 2022 Canadian Championship against FC Edmonton, first opening the scoring and then adding a penalty goal in a 2-1 victory.[12] This result seemed to give his play a boost after a slower start to the season, and Bevan scored in both of his next two matches.[13] In January 2023, Bevan signed a new two-year contract with Cavalry, with an option for 2025.[14]
The 2023 season proved much more fruitful for Bevan, as well as Cavalry. Cavalry finished regular season champions, winning the CPL Shield. Bevan scored 11 goals, sharing the Golden Boot with Atlético Ottawa's Ollie Bassett, and also added four assists.[15] Bevan would start the 2024 season by scoring Cavalry's first ever goal in the CONCACAF Champions Cup, during a 3-1 loss to Orlando City on February 27.[16] After the series with Orlando, he returned to New Zealand and did not return to the club for the beginning of their league season, citing personal reasons, with the club placing him on the Inactive roster list.[17]