He was spotted by Manchester United scouts while playing for St. Kevin's Boys, and joined the club's academy shortly after his 16th birthday in January 2008.

[6] He was named as an unused substitute for the first team's League Cup Fourth Round win at home to Wolverhampton Wanderers on 26 October 2010.

[18] Brady scored a first-half penalty in Hull's opening home Premier League match on 24 August 2013, giving them a 1–0 win against Norwich City.

[22] On 29 July 2015, Brady joined newly promoted side Norwich City on a three-year deal, for a reported fee of £7 million.

[23][24] He netted his first league goal in a Norwich City shirt on 26 September 2015, opening the scoring in a 2–2 draw against West Ham United at the Boleyn Ground.

[25] On 1 March 2016, Brady lost two teeth in a clash of heads with teammate Gary O'Neil in a Premier League match against Chelsea.

[29] On 31 December, Brady was sent off in the 0–0 draw at Brentford in a controversial decision with manager Alex Neil saying: "Robbie clearly isn't going in to injure the lad and both of them are sliding at impact, but we're not getting the rub of the green right now and that's just another example.

[31] He returned to the side for a 1–0 defeat by Southampton in the FA Cup on 18 January 2017[32] and scored a penalty in the following league match, a 3–1 win over Wolverhampton Wanderers.

[33] On 28 January, he made his final appearance for Norwich in a 2–0 win over Birmingham City, registering an assist for a Timm Klose goal just before half-time.

[34] On 31 January 2017, the final day of the January transfer window in England, Brady completed a move to Premier League club Burnley in a club record deal reportedly worth £13 million, meaning he would link up with his longtime friend Jeff Hendrick and international teammate Stephen Ward.

[36] Eight days after that, on 12 February, he scored his first Burnley goal, a 20-yard free kick, on his full debut for the club in a 1–1 home draw against league leaders Chelsea.

[37] In the following match on 25 February, Brady provided an assist for Michael Keane's equalising goal in the 1–1 draw away to Hull City, his former club.

[50] On 13 November 2015, Brady scored in the 82nd minute of the crucial Euro 2016 play-off first leg match against Bosnia and Herzegovina to earn a 1–1 draw.

[53] He also scored a penalty in Ireland's 2–1 defeat to the host nation, France, as The Boys in Green exited the tournament in the Round of 16 stage.