Sir Richard, Lord Rokeby and archbishop of Armagh, was immediately descended from the Robinsons of Rokeby in the north riding of the county of York, and was born in 1709. He was educated at Westminster school, from whence he was elected to Christ Church, Oxford, in 1726. In 1733 he took the degree of A. M., and in 1748 that of D. D. Dr Blackburne, archbishop of York, appointed him his chaplain, and collated him first to the rectory of Elton in the east riding of Yorkshire, and next to the prebend of Grindall in the cathedral of York. In 1751, he attended the duke of Dorset, lord-lieutenant of Ireland, to that kingdom, as his first chaplain, and the same year was promoted to the bishopric of Killala. A family connection with the earl of Holderness, secretary of state, with the earl of Sandwich and other noblemen related to him, opened the fairest prospects of attaining to the first dignity in the Irish church. Accordingly, in 1759 he was translated to the united sees of Leighlin and Ferns, and in 1761 to Kildare. The duke of Northumberland being appointed to the lieutenancy of Ireland in 1765, he was advanced to the primacy of Armagh, made lord-almoner, and vice-chancellor of the university of Dublin. When Lord Harcourt was lord-lieutenant of Ireland in 1777, the king was pleased, by privy seal at St James's, February 6th, and by patent at Dublin the 26th of the same month, to create him Baron Rokeby of Armagh, with remainder to Matthew Robinson of West Layton, Esq.; and in 1783 he was appointed prelate of the most illustrious order of St Patrick. On the death of the duke of Rutland, lord-lieutenant of Ireland, in 1787, he was nominated one of the lords-justices of that kingdom. Sir William Robinson, his brother, dying in 1785, the primate succeeded to the title of baronet. He was the survivor in the direct male line of the Robinsons of Rokeby, being the eighth in descent from William of Kendal. His grace died at Clifton near Bristol in the end of October 1794.