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.
[7] 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.
[12] 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.
[13] 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.
[14] 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.
[19] 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.
[25] On 4 August 2022, Byrne signed for Major League Soccer club Charlotte FC on a two-year contract with the option for a further year.