Connor was born about 1605, the second son of Daniel O'Brien and his wife Catherine FitzGerald.

His father's family, the O'Briens, were a Gaelic Irish dynasty that descended from Brian Boru, medieval high king of Ireland.

[7] Connor's mother was the widow of Maurice Roche, 6th Viscount Fermoy and the third daughter of Gerald FitzGerald, 14th Earl of Desmond,[8][9] and his second wife, Eleanor Butler.

Connor and Honora had a son: —and six daughters:[10] On 11 July 1662 when Charles II created his father Baron Moyarta and Viscount Clare,[11] O'Brien gained the courtesy title of Baron Moyarta.

On his father's death, which happened in 1663[12] or in 1666,[13][14] Moyarta, as he was now, succeeded as the 2nd Viscount Clare.