Edward Talbot died young in December, 1720, leaving a widow and child in poor circumstances. Rundle and he had lived together for ten years "in the most tender and endeared friendship." Their life in college and in the church promoted their social intercourse, "when absent our letters were the pictures of our souls and every post we conversed." Widow and daughter — the "dearest Kitty" of Rundle's letters, who afterwards became well-known as the friend and correspondent of Elizabeth Carter — lived as members of Seeker's household until his death in 1768 when they inherited from him a fortune of £13,000.
Bishop Talbot was translated to Durham in October 1721 and Rundle accompanied him as his domestic chaplain, retaining the archdeaconry and the treasurership in his old diocese of Salisbury. In his new situation he was even more amply rewarded. One of its well-endowed canonries was conferred upon him in January 1722 and a still better stall was bestowed upon him in November of that year. From 1722 he enjoyed the emoluments of the fat benefice of Sedgefield, and if he resigned that living in 1728 it was to succeed as master of Sherburn hospital, a desirable post in value and position, for it was situated less than two miles from the city of Durham. Hearne in his collections (viii., 100), calls him "a divine of 1500 libs per annum preferment who hath done or is about doing very honourably for Exeter college, having founded or being about to found and endow two Lectures there, viz., I in Natural Philosophy and I in Greek, each to be 50 libs per annum," but this rumour does not seem to have ended in fact.
During these years of quiet prosperity Rundle retained his old friendships and made fresh accessions to the list. Arthur Onslow, the famous speaker of the House of Commons, had sought his friendship "on the account of a public dispute he had against Tindal and Collins at the Grecian coffee-house
