Thomas Lindsay (or Lindesay, Lyndesay), D.D., B.D., M.A (1656–1724) was an Anglican clergyman who served in the Church of Ireland as the Dean of St. Patrick's Cathedral, Dublin, Bishop of Killaloe, Bishop of Raphoe and finally Archbishop of Armagh.
The son of a Scottish Minister, he was born in 1656 in Blandford in Dorset, England.
In 1686 he was appointed rector of St Mary Magdalene Woolwich in Kent (now London).
Two years later, he was nominated Bishop of Killaloe on 12 February 1696 and consecrated at St. Patrick's Cathedral, Dublin, on 22 March 1696 by Archbishop Narcissus Marsh of Dublin, assisted by Bishop William Moreton of Kildare, and Bishop Nathaniel Foy of Waterford and Lismore.
He was translated to the bishopric of Raphoe on 6 June 1713, and a few months later he was promoted to the archbishopric of Armagh on 4 January 1714.