The son of Sir William Clarke, he enrolled at Brasenose College, Oxford in 1676. He was elected a Fellow of All Souls College, Oxford in 1680. He was returned in a contested by-election on 23 November 1685 as Member of Parliament for Oxford University, but never took his seat as Parliament had been prorogued. He became Judge Advocate to the Army and was Secretary at War in Ireland from 1690 to 1692 and in England from 1693 to 1704 under William III of England and Queen Anne. He served as secretary to Prince George of Denmark, Queen Anne's consort and the Lord High Admiral and Generalissimo of England. Clarke was returned as Member of Parliament for Winchelsea at the 1702 English general election, coinciding with his office as Joint Secretary of the Admiralty. At the 1705 English general election he was returned as MP for East Looe. He was not nominated for a seat at the 1708 British general election. He was returned in a by-election on 29 May 1711 as MP for Launceston from 1711. He did not stand at the 1713 British general election. Over the latter period he was Lord Commissioner of the Admiralty from 20 December 1710 until 14 October 1714, when he was dismissed following the accession of George I. Clarke returned to the House of Commons as MP for Oxford University at a by-election on 4 December 1717. He was reelected in the general elections of 1722, 1727 and 1734. By the time of his last election in 1734 he had lost his left eye and was losing sight in the other. He was also an amateur architect. His known work is largely confined to Oxford, and he is known to have designed buildings and also to have collaborated with Nicholas Hawksmoor, amongst others. Timothy Clayton discusses Clarke's print collection, noting “John Vanburgh, Alexander Pope and George Vertue travelled to Oxford to use his library with its unique collection of notes and drawings by Jones”. The library of Worcester College, Oxford houses Clarke's collection of books, MSS, prints and drawings. Building work on the library, which was started within a few years of the college's founding in 1714, was completed in 1736. A spat between Clarke and All Souls resulted in the bequest to Worcester.
