Cardiff Rugby Beetham was part of the Cardiff academy until under-18 level. He departed the academy and played for
Glamorgan Wanderers, before rejoining the academy during the 2019–20 season. Beetham was named in the Cardiff academy squad for the
2021–22 season. He made his debut for Cardiff in the first round of the
2021–22 European Rugby Champions Cup against
Toulouse, starting at full-back. During the match, he received a red card for a high tackle, and was subsequently banned for three weeks. In September 2022, while playing for
Cardiff RFC, Beetham suffered an ACL injury which ruled him out for the remainder of the season. Ahead of the 2023–24 season, Beetham signed an extension with Cardiff's academy, while training with the senior squad. On 2 February 2024, Beetham signed a new contract with Cardiff. Beetham has shown his versatility while playing for Cardiff, covering inside centre, wing, and full-back all in the opening rounds of the
2025–26 United Rugby Championship. Beetham signed an extension again, on 28 April 2026. ==International career==