Byrne played for St Albans City as a youth player, before becoming a Tottenham Hotspur player, signing professional forms in June 2010. In February 2011, he was loaned out to Brentford of League One. He made his senior debut on 26 February, replacing Myles Weston 77 minutes into a 1–0 home win over Bristol Rovers. He won his first start at Griffin Park on 8 March, playing in a 1–0 defeat to Brighton & Hove Albion. He was singled out for praise for his performance against Brighton by manager Nicky Forster. On 28 July 2011, English League One club Bournemouth signed Byrne on loan until the end of the season. In a match against Exeter on 17 September 2011 Byrne suffered an ankle injury that would keep him out of action until the new year, he chose to remain at Bournemouth for treatment. On 22 February 2012, Byrne was recalled to Tottenham having made his return from injury in a Spurs XI friendly the day before. Byrne was signed by Crawley Town on loan on 24 September 2012 till 6 January 2013. He made 14 starts and 1 substitute appearance, scoring once, his first ever league goal, at Carlisle United on 29 September 2012.
Swindon Town (loan and permanent transfer)
On 28 March 2013, Byrne signed for Swindon Town on a loan deal that would see him at the County Ground for the rest of the 2012–13 season. On 26 April 2013, Nathan agreed to sign for Swindon Town on a free transfer following a successful loan spell at the club from Tottenham Hotspur. During the second leg of the League One playoffs against Brentford, he received a red card during extra time after Swindon equalised late in the first half to make the score 3–3. Byrne made 43 league appearances during the 2014–15 season and helped Swindon make the play-offs. having contributed 3 goals and 9 assists in the league, he also made the League One team of the year.
During the first leg of the League One play-off semi final against Sheffield United away, he scored the winning goal for Swindon on 93 minutes to make the score 2–1 and carry a one-goal advantage back to the County Ground. Byrne scored a hat-trick on the opening day of the 2015–16 season in a 4–1 win against Bradford City.
Wolverhampton Wanderers
On 1 September 2015 Byrne joined Championship club Wolverhampton Wanderers, signing a three-year contract for an undisclosed fee. He made his club debut on 19 September 2015 as a substitute in a goalless draw against Brighton, with his first start coming later that month in a 3–0 win at Fulham. Byrne scored his first goal for the club on 17 December, a late consolation in a 2–3 home loss to Leeds United. His second and final goal for the club also came at Molineux, when he opened the scoring in a 2–1 win over Bristol City on 8 March 2016. What was to be his final appearance for the club came as a late substitute in a 1–1 draw at eventual champions Burnley on 19 March, where his last-minute corner was headed in by Danny Batth.
Wigan Athletic
On 31 August 2016, almost a year after joining Wolves and having not featured under new coach Walter Zenga, Byrne departed to join newly promoted Championship side Wigan Athletic for an undisclosed fee in a three-year deal. On 9 January 2017 it was announced that Byrne had joined League 1 side Charlton Athletic on loan for the remainder of the season. He scored his first goal for the club in a 2–1 win over Bolton Wanderers on 28 January 2017. In April 2019 Byrne was subjected to racist tweets.
