Career
Byrne began his professional career with Tottenham but never made a first team appearance for the club before leaving to join League One Swindon Town in 2013. After two full seasons with the Robins, during which they reached the 2015 Football League One play-off Final he was bought by Championship side Wolverhampton Wanderers. Tottenham Hotspur
Byrne played for Street Albans City Youth F.C. 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 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
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 2012-2013 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 2014-2015 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 F.C. 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.
Wolves
On 1 September 2015 Byrne joined Championship club Wolverhampton Wanderers, signing a three-year contract (with the option of a fourth year) for an undisclosed fee. He made his club debut on 19 September 2015 as a substitute in a goalless draw against Brighton.