Richard, distantly related to the preceding, was the son of Mr Richard Pococke, head master of the free school at Southampton, where he was born in the year 1704. He received his school learning under his father, and his academical education at Corpus Christi College, Oxford, where he took his various degrees. He commenced his travels in the East in 1737, and returned in 1742. In 1743 he published his Observations on Egypt, under the general title of A Description of the East and some other Countries. In 1744 he was made precentor of Waterford; and in 1745 he printed the second volume of his Travels, under the title of Observations on Palestine, or the Holy Land, Syria, Mesopotamia, Cyprus, and Candia, which he dedicated to the Earl of Chesterfield, then lord-lieutenant of Ireland, whom he attended in the capacity of domestic chaplain. In 1755 Dr Pococke was promoted to the bishopric of Ossory, vacant by the death of Dr Edward Maurice; in July 1765 he was translated to the see of Meath, which had been originally intended for the Bishop of Elphin, who, however, declined taking out his patent; and he died suddenly in September following, having been carried off by apoplexy, whilst engaged in visiting his diocese. As a traveller, Dr Pococke was equally distinguished for research, learning, and accuracy, to which ample justice has indeed been done by Jablonski, in the Preface to part third of his Pantheon Aegyptiorum. He penetrated farther up the Nile than the island of Philae, called by the Arabs the Temple Island; whereas Norden, in 1737, proceeded as far as Derre, between the first and second cataracts. The two travellers are supposed to have met on the Nile, in the neighbourhood of Esneh, in January 1738; but, according to another account, they passed in the night without recognition.

Bishop Pococke visited other parts besides the East, and described some remarkable objects both in Scotland and Ireland. A French translation of his Travels appeared at Paris, 1771, in 7 vols. 12mo.