He won his first Listed race on the Flat, the National Stakes at Sandown, with Taras Girl in 2000, but had to wait another six seasons before he won his next big race, the Lincoln, which was run that year at Redcar, with Blythe Knight in 2006. Crow Wood won the Grade 2 Elite Hurdle at Wincanton for the yard in November that year and a steady stream of high-profile winners followed.
Blythe Knight proved admirably versatile, winning the Top Novices' Hurdle at Aintree in early 2007, in the days when it was still a Grade 2 contest, and the Group 3 Diomed Stakes at Epsom that season and the next, to provide Quinn with his first Pattern race winners on the Flat. Other notable National Hunt winners included Character Building in the Fulke Walwyn Kim Muir Challenge Cup at the Cheltenham Festival in 2009 and his first Grade 1 winner, Countrywide Flame, in the Triumph Hurdle in 2012.
On the Flat, Quinn saddled the first of his seven Group 2 winners, Red Duke, in the Superlative Stakes at Newmarket in 2011 and his one and only Group 1 winner, The Wow Signal, in the Prix Morny at Deauville in 2014.