Career
Celtic
Nesbitt is a product of the academy system at Celtic. On 21 May 2015, Nesbitt scored a hat-trick in the 2015 SFA Youth Cup final against Rangers. On 23 September 2015, Nesbitt made his first team debut in a League Cup match against Raith Rovers when he came on in the 89th minute.
Partick Thistle
On the 1 February 2016 Nesbitt joined fellow Scottish Premiership side Partick Thistle on loan until the end of the 2015-2016 season.
Nesbitt was named in the team of the tournament at the 2014 Union of European Football Associations European Under-17 Football Championship, as Scotland under-17s reached the semi-finals. He then appeared for the Scotland under-19 team in each of the following two seasons.