He was the son of William James Conolly of Castletown House, by his wife Lady Anne, daughter of Thomas Wentworth, 1st Earl of Strafford. In 1758 he married Lady Louisa Lennox, daughter of Charles Lennox, 2nd Duke of Richmond. They had no children.
He sat in the Parliament of Great Britain for Malmesbury from 1759 to 1768 and for Chichester from 1768 to 1780. In 1761 he was elected to the Parliament of Ireland for Ballyshannon and for County Londonderry, sitting for the latter constituency until May 1800. On 6 April 1761 he was appointed to the Privy Council of Ireland.
On his death Wentworth Castle was inherited by Frederick Thomas William Vernon, grandson of the 1st Earl of Strafford"s daughter Harriet.
Castletown House passed to his widow Lady Louisa and then to Edward Pakenham, grandson of Conolly"s sister Harriet, being sold by William Conolly-Carew, 6th Baron Carew in 1965.
11th Parliament of Great Britain. 12th Parliament of Great Britain. 13th Parliament of Great Britain.
14th Parliament of Great Britain]
In Dublin, Conolly was a member of the Kildare Street Club.
