Conway came through the Bolton Wanderers academy, joining at U16 level. He signed his first professional contract with Bolton Wanderers on 13 June 2022.[3]
Prior to signing his deal, Conway had featured on the first team bench during the 2020–21 season and was amongst the substitutes for the EFL Trophy Group stage game against Shrewsbury Town in October 2020.[4]
National League loan spells
In November 2022, Conway joined National League North club Buxton on loan until January 2023,[5] and the following February, he extended his loan deal with the club until the end of the season.[6] In May 2023, Bolton announced that Conway had signed a new one-year deal with the club.[7]
In August 2023, Conway was loaned out to newly relegated National League side, Rochdale,[8] On 6 October after featuring just seven times for Dale, he was recalled by parent club, Bolton Wanderers.[9]
A day later, Conway joined fellow National League club AFC Fylde on a 28-day loan deal;[10] his loan was extended in November until 31 January 2024,[11] and then until the end of the season.[12] On 22 May 2024, Bolton confirmed that they had activated an option to extend his contract with the club.[13]
Crewe Alexandra (loan)
On 9 August 2024, despite featuring heavily for Bolton's first team during pre-season, Conway joined League Two side Crewe Alexandra on a season-long loan.[14] Conway made his senior debut in the EFL a day later, coming on as a substitute for Lewis Billington during Crewe's 1–0 defeat at Barrow on the opening day of the season.[15] He scored his first senior goal (a "fine individual effort") in Crewe's 1–1 League draw at Doncaster Rovers on 12 October 2024.[16]