Connesburgh, Edmund (a.1445–c.1480), archbishop of Armagh, was appointed in an attempt to end the financial crisis that faced the diocese after the archbishopric of John Bole (qv). Connesburgh was an Englishman and a servant of Edward IV who had been sent to Rome on an embassy by the king. His predecessor in Armagh, John Foxhals (qv), had died in October 1474, unable to pay the debts owed to the pope for his election. Connesburgh was acceptable to both the king and the pope, and was provided to the see in June 1475, after another candidate, Richard Lang, bishop of Kildare, had been withdrawn. Lang, the candidate of the chapter of Armagh, was almost certainly supported by Thomas fitz Maurice FitzGerald (qv), 7th earl of Kildare. Connesburgh agreed to pay his own debts and those remaining from Foxhals, but it took him almost two years to arrange the needed loans. He was in London in June 1477; the king restored the temporalities of the see to him in July, and gave him a force of 200 soldiers to deliver to the deputy lieutenant in Ireland.
Connesburgh arrived in Ireland in August 1477 and called a meeting of the chapter in Dundalk in September. His position within his see was undermined by the presence of the apostolic administrator Octavian de Palatio (qv), who had been sent by the pope to investigate the ruinous finances of the diocese. Connesburgh asked to be allowed to govern his see, but the chapter stuck to the letter of the law and refused him on the grounds that he had not paid the debts owed to the pope, even though he had been given access to the temporalities of the see. He then entered into negotiations with Octavian, and in November 1477 they reached an agreement under which Connesburgh agreed to resign his see in favour of Octavian in return for a yearly pension and the payment of his outstanding debts by the apostolic administrator. He was still acting as archbishop at Christmas 1477 and intervened to make the transfer of the diocese to Octavian smoother in the face of some opposition by the new deputy lieutenant, Gerald FitzGerald (qv), 8th earl of Kildare. Connesburgh returned to England after May 1478 and died there c.1480.