Born in Meath, Ireland, Darragh was brought to England by Blackburn Rovers as a 17-year-old after developing at Irish youth side Belvedere.

Promoted to the senior set-up in 2012, Darragh joined then-League Two outfit Burton Albion on an initial months loan in October 2014, making his EFL debut against Stevenage.

Following an extension to his loan deal, he scored his first career goal, a late equaliser away at Portsmouth, at the turn of the year before being called back by Blackburn in March for the remainder of the campaign.

Darragh made his Rovers debut in April 2015 – coming on as a sub against Millwall at Ewood Park – and followed that by making his first start against Huddersfield a week later.

Blackburn were relegated at the end of the 2015/16 season, but Darragh picked up a League One promotion winners medal the following year after opting to stay at Ewood Park.

Darragh has represented his country at all levels from U17 and made his senior debut in 2018 against the USA.

He was a mainstay at Blackburn following their return to the Championship and was named club captain for the 2021/22 season.

Blackburn announced his departure in June 2022, just days after he returned to the Republic of Ireland side for the first time in four years, against Ukraine in the Nations League.

Darragh joined Boro on 24 June 2022.