While part of the Dragons Academy, Dyer made his professional debut on 27 January 2018, against Saracens in the Anglo-Welsh Cup.[2] His first appearance in the Pro14 came against Benetton Rugby the following month.[3]
Dyer was named man of the match on 4 January 2020, as the Dragons beat regional rivals Ospreys 25–18, with Dyer scoring a try in the victory.[4] In March 2020, Dyer signed his first professional contract with the Dragons.[5] He signed an extension in January 2022.[6]
On 23 October 2022, Dyer again claimed a man of the match award against the Ospreys, scoring twice and propelling the Dragons to a 32–25 win.[7]
On 17 January 2024, Dyer signed a long–term contract extension with the Dragons.[8]
On 18 October 2022, Dyer was named in the Wales squad for the 2022 Autumn series.[11] Dyer started against New Zealand on 5 November 2022, and scored the first try for Wales.[12]
Dyer scored his second try for Wales in the final match of the series, a loss against Australia.[13]
Owing to his continued good form, Dyer continued his involvement with the national side, and was named in the Welsh squad for the 2023 Six Nations Championship.[14] Dyer started the first two matches against Ireland and Scotland, but was dropped for the match against England, following Louis Rees-Zammit returning to fitness.
Recalled to the starting team against Italy, he scored his third try for Wales, and secured his first win for the national side.[15] The following week Dyer scored again, against France, securing a try bonus point for Wales as they avoided a wooden spoon finish.[16]
Dyer was named in the Wales squad for the 2023 Rugby World Cup, and appeared in all matches as Wales made the quarter final round.[17]