Conway made his professional debut on 25 February 2017, scoring a four-round points decision (PTS) victory against Sonny Whiting at the Civic Hall in Bedworth, Warwickshire.
[3] After scoring five more wins, two by stoppage, he defeated Chris Monaghan via seventh-round technical knockout (TKO) to capture the British Challenge middleweight title[4] on 9 March 2018 at The Deco in Northampton.
[7] He bounced back from defeat on 25 May with a four-round PTS victory against Harry Matthews,[8] before challenging British super-welterweight champion Ted Cheeseman on 21 June at the York Hall in London.
[10] Conway ended 2019 with PTS victories against Konrad Stempkowski in October and Craig O'Brien in December,[11][12] before facing his friend and former sparring partner Navid Mansouri for the vacant WBA Inter-Continental super-welterweight title on 14 August 2020 at Matchroom Sport's headquarters in Brentwood, Essex.
[14] His final fight of 2020 was originally scheduled to be against Olympic bronze medallist Souleymane Cissokho on 12 December at The SSE Arena in London, with the bout serving as part of the undercard for Anthony Joshua vs. Kubrat Pulev.