Conway biggest boxing bout of his career was challenging for the WBO Asia Pacific light heavyweight title against Soulan Pownceby in June 2011.
Conway has refereed and judged in many notable boxers including Chauncy Welliver, Michelle Preston, Daniella Smith, Gunnar Jackson, Robert Berridge, Shane Cameron, Jeff Horn, Izuagbe Ugonoh, Kali Meehan, Brian Minto, and Joseph Parker.
[4] Outside being an official, Conway owns his own gym called Rebel Lee Gar and trains many successful boxers and kickboxers including Adrian Taihia, Baby Nansen, Lani Daniels, Richie Hardcore and David Letele.
In February 2017, Lance Revill resigned as president of NZPBA due to the backlash of the comments made against World Champion Joseph Parker.
[7] When setting up Daniels first world title fight, Conway was in negotiations with opponent Alrie Meleisea manager Vasco Kovačević since Christmas day 2022.