[1] Bealham moved to Ireland in 2010 and initially played in his grandmother's native province of Ulster with the amateur side, Belfast Harlequins.

[6] In April 2014, it was announced that Bealham had signed a professional contract with the province to last until summer 2015, making him a full member of Connacht's senior squad.

[7] In the 2014–15 season Bealham was moved from loosehead to play tighthead by Connacht forwards coach Dan McFarland.

Bealham made his European debut on 6 December 2014, coming on from the bench in the home game to Bayonne in the Challenge Cup pool stages.

[13] Bealham was again a key part of Connacht's squad for the 2015–16 season, being the only player to feature in all 31 of the team's games in the league and in Europe.

[6][11][15] On 28 May 2016, Bealham started in the Pro12 Grand Final as Connacht won 20–10 against Irish rivals and reigning champions Leinster to claim the team's first major trophy in their 121-year history.

[1][2] After becoming aware of his qualification to play for Ireland, Bealham became involved in the country's youth set-up through the Irish Exiles program.

[24] He played in two of the team's fixtures, replacing Stephen Archer in the games against Emerging Italy and Georgia, scoring a try in the latter.

[30][31] Bealham had been due to play in the first test of the 2022 Ireland rugby union tour of New Zealand at Eden Park in Auckland on 2 July but COVID-19 meant he could not.