Anthony was educated at Mr. Young's school in Abbey Street, Dublin, and on 6 April 1720 was admitted a gentleman-commoner of Christ Church, Oxford.

His treatment was regarded as too severe by William Pitt; and Malone, who drew a distinction between advice offered in council and his conduct in parliament, introduced the measure as chairman of the committee of supply.

[1] Malone supported John Monck Mason's bill for enabling Roman Catholics to invest money in mortgages on land.

In 1762 he was appointed, with Sir Richard Aston, to try the Whiteboys of Munster; they agreed in ascribing the rural violence to local and individual grievances.

By his will, made in July 1774, he left all his estates in the counties of Westmeath, Roscommon, Longford, Cavan, and Dublin to his nephew, Richard Malone, 1st Baron Sunderlin as he became, eldest son of his brother Edmund.

On his death without issue in 1816, and his brother Edmund junior also having died without heirs, the right of succession to the family estates was disputed, due it was said to Anthony's will being so badly drafted.