Thomas Dickson-Peters played for Norwich's Under-18s as a substitute in their 2-0 defeat to Southampton on 10th February 2018. He is also a promising athlete from Berkshire who had trials with Liverpool, Manchester City, Crystal Palace and Fulham before joining Norwich.

He was called up to the Scotland Under-17 squad in August 2018 and played two games against Russia in Spain; scoring in the second a 2-0 win. The 2018/19 season started with him making appearances for the Norwich City Under-18s. He also scored for Scotland's Under-17s in a 1-1 draw with Poland in March 2019.

Dickson-Peters made 13 competitive appearances for the Under-18s in 2018/19, scoring five times

Tom signed his first professional contract with Norwich on 17th October 2019. .He said “It’s a really great feeling, I’m honoured to be given the chance to sign the contract up. I’m very happy being given the opportunity at the club.It’s great to see all the players in the first team coming in from the academy, as a young player it’s inspiring and great to see where you could end up, and hopefully where I end up.Signing a professional contract is a huge milestone for every footballer, especially at such a young age. Looking back on his years of hard work, there isn’t much that the striker would change, apart from living in the moment a bit more. Looking back, the only advice I’d give myself is to just work hard and be happy. Every day playing football, it’s such a great opportunity that you can’t take for granted.”

On 16th September 2020 (his 18th birthday) he signed a new three-year professional contract with Norwich. This came days after scoring a hat-trick for Norwich's Under-18s in their 5-1 opening day victory over West Brom. He scored nine goals in 21 games for City’s U18s in 2019/20. Norwich's injury crisis in November 2020 saw Tom on the bench for Norwich's clashes with Stoke City and Coventry City. He was next included on the bench for City's Premier League clash with Aston Villa on 14th December 2021 following a Covid outbreak in the first team squad.

On 4th January 2022 Tom joined League One side Gillingham on loan until the end of the season. Gills boss Steve Evans said “I met young Tom and the people from Norwich City yesterday. The young man had a number of clubs he could have joined, such is his talent, but I got a call late afternoon yesterday to say he wanted to come to Gillingham.It obviously helps Norwich City favour us as his destination when you consider the development that the likes of Chris Wood, Jack Marriott and Ivan Toney made working with Paul and myself. Tom is the Premier League 2’s leading goalscorer with 18 goals in league and cup action. I have watched his progress since the start of the season and it’s an exciting journey he is on. He is a lovely kid who wants to continue scoring goals and we will do everything to help him.”

Tom made his Gillingham (and League debut) on 8th January 2022 coming on as a half-time substitute in a 4-0 home defeat to Ipswich. He then signed a new contract with Norwich until 2025. Dickson-Peters made nine appearances as Gillingham were relegated from League One.

On 31st January 2023 he was loaned to League Two side Grimsby for the remainder of the 2022/23 season. He scored on his debut against Crewe on 4th February 2023 which was a 3-0 away win. He played four games in total for the Mariners but didn't add any further goals.

At the end of September 2023 he was loaned to National League side Woking on an initial one month loan.

Tom and Norwich parted company by mutual consent on 8th November 2023.