Born in England to an English father and a Greek Cypriot mother, he began his senior career at Tottenham Hotspur, where he made one substitute appearance in the EFL Cup.
[10] On 20 September 2016, Mauricio Pochettino likened Edwards to a young Lionel Messi due to his low centre of gravity and ability to beat a man.
[11] The next day Edwards made his competitive debut in the EFL Cup third round at home to Gillingham, coming on as a substitute for the final 15 minutes in place of Vincent Janssen and taking a shot that was saved by Stuart Nelson in a 5–0 win.
[18] He made his Norwich City debut on 30 March, coming on as a late substitute for Mario Vrančić, in a 2–0 home loss against Fulham.
[25] On 2 September 2019, Portuguese Primeira Liga club Vitória de Guimarães signed Edwards on a four-year deal, purchasing 50% of his economic rights and setting a €15 million buyout clause.
[26] He scored his first goal on 24 October in the UEFA Europa League group stage, opening a 3–2 loss at his former club's rivals, Arsenal.
[28] He and João Carlos Teixeira both scored twice on 8 February 2020 in a 7–0 win at local rivals Famalicão, who were in contention for a Europa League place.
[32] Edwards was transferred to reigning Primeira Liga champions Sporting CP on 31 January 2022 for a fee of €7.67 million with a further €500,000 if certain objectives are met.
Sporting bought the 50% of his economic rights held by Vitória, while sending Bruno Gaspar and Geny Catamo in the opposite direction, on a permanent basis and a loan respectively.
[37] In Sporting's run in the 2022–23 Taça da Liga he scored in a 6–0 rout of Farense in the first group game,[38] and a 5–0 quarter-final win against Braga also at the Estádio José Alvalade;[39] he started in the final on 28 January, a 2–0 loss to Porto in which he had a goal ruled out for offside.
[42] On 8 February, Edwards scored in his club debut, netting the only goal in a victory over Southampton in the fourth round of the FA Cup.