[1] Carmarthen–born Price attended Ysgol Bro Myrddin, and began his rugby career with local team Carmarthen Quins.
He played for the Quins through all age grade levels, and represented their first team before featuring for the Scarlets.
[7] Price made five appearances for the side, before returning to the Scarlets for the Pro14 Rainbow Cup.
[9] On 21 April 2023, Price signed another contract extension with the Scarlets, along with fellow lock Morgan Jones.
[10] Price’s younger brother Elis has also represented Wales U20 and the Carmarthen Quins, while part of the Scarlets academy.