Nelson was a youth product of Tottenham Hotspur from the age of 7 to 15, before finishing his development with Luton Town after a successful trial. He rose up their youth categories and started training with their senior team in September 2022. On 6 March 2023, he signed his first development contract with Luton Town. On 31 January 2024, he extended his contract with the club. Nelson made his senior and professional debut with Luton Town as a late substitute in a 1–1 Premier Leaguedraw with Crystal Palace on 9 March 2024.