Arthur Annesley was the son of Francis Annesley Lord Mountnorris, and Dorothy Phillips. He was born at Dublin 10 July 1614. In 1624 he was sent to England, and in 1630 admitted to Magdalen College Oxford where he took his degree in 1634 and entered Lincoln's Inn. After the grand tour he returned to Ireland. In 1647 he was elected to the Long Parliament for the county of Radnor. He was entrusted with missions for Parliament in 1645 and 1647. He was one of the members secluded from Parliament in 1648. In Richard Cromwell's Parliament in 1658 he sat for the City of Dublin and with other secluded members attempted to get admission to the Rump Parliament in 1659. He was in the confidence of the Royalist party, though a Presbyterian sympathiser. In February 1660 he was chosen President of the Council of State, and took a prominent part in the Restoration. In August 1660 he received his father's office of Vice-Treasurer and Receiver-General for Ireland. On his father's death in November 1660 he became Viscount Valentia and was created Lord Annesley of Newport Pagnell in Buckinghamshire and Earl of Anglesey. He was Treasurer for the Navy and Lord Privy Seal, and was very outspoken on matters of conscience. On 9 August 1682 he was dismissed from the post of Lord Privy Seal He retired to his estate of Blechingdon and took little further part in affairs. He died of a quinsy 26 April 1686. He formed a great library which was sold by Thomas Philipps in London 25 October 1686.