 His MCCA Knockout Trophy debut for Cumberland also came in 2008 against Shropshire, with Conway making eight further appearances in that competition to 2010.He left Cumberland at the end of the 2010 season, joining Herefordshire two years later, making his debut for his new county against Wiltshire in the 2012 Minor Counties Championship.In the 2010 season, he made his first-class debut for Oxford MCCU against Northamptonshire at the University Parks, making two further first-class fixtures in that season against Hampshire and Middlesex.