Neilson has previously played for Dundee United, as well as on loan for Falkirk, Partick Thistle and St Johnstone.
[2] After graduating from the club's academy,[2] he made his professional debut in a 1–1 draw against St Johnstone on the opening day of the 2020–21 Scottish Premiership season.
[9] On 3 August 2023, Neilson joined Scottish Championship club Partick Thistle on a season-long loan.
[12] On 30 July 2024, Neilson joined Scottish Premiership club St Johnstone on loan for the 2024–25 season.
[13] Neilson was recalled early from his loan at St Johnstone, by his parent club Hearts on the 1st of January 2025.