Sir Thomas Norris (Norreys) (1556–1599) was an English soldier, made Lord President of Munster in Ireland.
He was the fifth son of Henry Norris, 1st Baron Norreys, of Rycote House and Wytham Abbey in Oxfordshire (the latter previously in Berkshire), and his wife, Margery, the youngest daughter of John Williams, 1st Baron Williams of Thame. He matriculated at Magdalen College, Oxford, in 1571, aged 15, graduating Bachelor of Arts on 6 April 1576. Sir John Norris, and Sir Edward Norris were his brothers. He married Bridget, daughter of Sir William Kingsmill of Sydmonton in Hampshire, by whom he had one daughter, Elizabeth, his sole heiress, who married Sir John Jephson of Froyle in Hampshire. Their son William Jephson sat in the Long Parliament.
In December 1579, he became, through the death of his eldest brother, William, and the influence of Sir William Pelham, captain of a troop of horse in Ireland. He took an active part in the following year in the campaign against Gerald FitzGerald, 15th Earl of Desmond; but during the absence of Sir Nicholas Malby, Lord President of Connaught, in the winter of 1580-1, he acted as governor of that province, and pursued the Burkes and other disturbers of the peace. In 1581-2 he was occupied, apparently between Clonmel and Kilmallock, in watching the movements of the Earl of Desmond, and on the retirement, of Captain John Zouche in August 1582, on account of ill-health, he became colonel of the forces in Munster. He compelled the Earl of Desmond to abandon the siege of Dingle, but he lacked the resources to do more. In consequence of the appointment of Thomas Butler, 10th Earl of Ormond as governor of Munster, Norris was able, early in 1583, to pay a brief visit to England. On his return he found employment in Ulster in settling a dispute between Hugh Oge O'Neill and Shane MacBrian O'Neill as to the possession of the castle of Edendougher (Shane's Castle), which he handed over to the latter as captain of Lower Clandeboye. He was commended by Lords-justices Adam Loftus and Henry Wallop. In the autumn of 1584 he took part in Sir John Perrot's expedition against the Scots in Antrim, and in scouring the woods of Glenconkein in search of Sorley Boy MacDonnell he was wounded in the knee with an arrow.