*Club domestic league appearances and goals, correct as of 18:00, 3 February 2024 (UTC) ‡ National team caps and goals, correct as of 23:49, 26 July 2021 (UTC)
Norburn played as a youth team player with Chelsea before moving to Leicester City, where he graduated through to the professional ranks in 2011.[3] He joined Bristol Rovers on a month-long loan deal in late September 2011,[4] later extended to three months, where he played alongside fellow on-loan Leicester teammate Cian Bolger.[3]
He made his debut in senior football on 14 October 2011, when he was an 86th-minute substitute for Bristol Rovers in a 5–2 victory over Rotherham United.[5] By the end of December, Norburn returned to Leicester City after his loan-spell at Bristol Rovers finished and spent the rest of the season staying at Leicester City. On 3 July Norburn signed with the Bristol Rovers on a permanent basis, and agreed to sign a one-year deal with the option for a further 12 months with the club.[6] On the opening game of the season, Norburn made his debut in a 2–0 loss against Oxford United. Two months later, he scored his first goal in a 3–1 win over Northampton Town.[7] His second goal came on 5 February 2013, in a 1–1 draw against Cheltenham Town and his third was followed up a month later, in a 2–1 win over Exeter City. At the end of the 2012–13 season, Norburn was offered a new contract by the club,[8] where he signed a one-year contract extension on 24 June 2013.[9]
In the 2013–14 season, Norburn had his first team opportunities limited, making sixteen appearances. On 4 April 2014, he left Bristol Rovers by mutual consent. First team manager Darrell Clarke said of Norburn leaving: "Ollie has left the club, and that was mutually agreed. For whatever reason it has not gone well for Ollie this season. Ollie has a chance now to try and earn himself a contract at another club, and we wish him well and thank him for his efforts."[10]
On 23 July 2014, Norburn signed for Plymouth Argyle as a free agent on a one-year deal. He was released by Plymouth at the end of the 2014–15 season having failed to establish himself in the first team.[11] He started training with Guiseley in late 2015, and then signed for the club after impressing manager Mark Bower in the sessions.[12] On 27 February 2016 Norburn scored a controversial goal for Guiseley in a National League match against Braintree Town, after Braintree Town had put the ball out for a player to receive treatment. The goal stood and Guiseley drew the game 1–1.[13]
Norburn joined Macclesfield Town of the same league in July 2016.[14] He scored eight goals in his sole season with the Silkmen, including one in each leg of their FA Trophy semi-final win over Tranmere Rovers and one more in the 3–2 loss to York City in the final, before signing a three-year contract with Tranmere.[15]
On 9 August 2018, after winning promotion to League Two with Tranmere via the play-offs, he signed a three-year deal to move to Shrewsbury Town, led by his former Macclesfield manager John Askey.[16] He signed a new contract with Shrewsbury in July 2019.[17]
