Claire's father, Evan Molloy, is a prominent member of the Colaiste Iognáid (Jez) Rowing Club.

Her younger brother, Tim Molloy, is a former Republic of Ireland under-19 association football international and also played for University College Dublin A.F.C.

[9] On 2 October 2005 she played in the 2005 All-Ireland Senior Ladies' Football Championship final which Cork won 1–11 to 0–8 [10] Other members of these Galway teams included Niamh Fahey and Annette Clarke.

[13] Molloy switched codes from Ladies' Gaelic football to women's rugby union while attending Cardiff University where she studied medicine.

[5] She was also a Cardiff Quins player when she made her debut for the Ireland women's national rugby union team.

[14][15] Molloy subsequently joined Bristol Ladies and on summer trips home from university she also played for Galwegians.

[11][16] Together with Sarah Hunter and Carys Phillips, Molloy was one of three Bristol Ladies players to captain their countries at the 2017 Women's Rugby World Cup.

[20][21] On 6 February 2009, Molloy made her debut for the Ireland women's national rugby union team when she came on as replacement in a 7–5 win against France.