Darragh started competing at 10 years old, riding at the Junior European Championships and the Young Rider European Championships. He competed as a member of the Irish Jumping Team at the 2014 Alltech FEI World Equestrian Games, earning 12th place. While competing on the European circuit, Darragh was an integral part of the Irish team that won the 2015 Nations Cup CSIO 5*.
Darragh's career has gone from strength to strength and in 2021, he posted a series of top results including 4th in the 5* Grand Prix of Geneva and 4th in the LGCT Super Grand Prix at the GC Prague Playoffs, dropping only one fence across the two rounds, as well as 6th in the LGCT Grand Prix of Samorin. He also competed in the 2020 Tokyo Olympics for Ireland, placing 17th individually.