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 1580–81, he acted as governor of that province, and pursued the Burkes and other disturbers of the peace. In 1581–82, 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
Shane's Castle (Edendougher), 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
Glenconkeyne in search of
Sorley Boy MacDonnell he was wounded in the knee with an arrow. He returned to Munster, and in 1585–86 represented
County Limerick in
Parliament. In December 1585, he was appointed vice-president of Munster during the absence in the Low Countries of his brother John. It was a precarious situation. Under instructions from England, Norris, in March 1587, arrested
James Fitzedmund Fitzgerald,
seneschal of
Imokilly,
Patrick Condon, and others, whose loyalty was at least doubtful. The marriage of Ellen, daughter and sole heiress of
Donald McCarthy, 1st Earl of Clancare, was a politically sensitive topic and Norris himself rejected her as his bride. In June 1588, the matter became serious, when
Florence MacCarthy married her and so united in himself the two main branches of the
clan Carthy. Norris arrested Florence, but was induced to believe that he had acted innocently. In December he was knighted by Sir
William Fitzwilliam; and Sir
John Popham having consented to resign his
seignory in the plantation of Munster, Norris obtained a grant of six thousand acres (24 km2) in and about
Mallow. The
Spanish Armada was over but the air was still full of rumours of invasion, and in 1589–90 Norris was engaged with
Edmund Yorke, an engineer who had been sent over from England expressly for the purpose, in strengthening the fortifications of Limerick,
Waterford, and
Duncannon. He lacked cash, and a detachment at Limerick in May 1590 mutinied and marched to
Dublin. The ringleaders were punished by Sir William Fitzwilliam. Norris was in the winter of 1592–93 in England to report on the Munster plantation; he returned to Ireland about May 1593. With the exception of disturbances over the summer by Donogh Mac Carthy, the Earl of Clancare's illegitimate son, the province was peaceful. On 10 August 1594, Norris went to Dublin to meet the new lord-deputy, Sir
William Russell, whom he attended in his progress through Ulster. In the following year he served under his brother, Sir John Norris, against the
Earl of Tyrone, and was wounded in the thigh in the engagement that took place halfway between
Newry and
Armagh on 4 September. He assisted Sir John Norris as commissioner for the pacification of
Connaught in June 1596, but, in August, he was engaged in repelling an incursion of the MacSheehys and O'Briens into Munster. He hanged ninety of them within ten days, but they proved tenacious. He again in September accompanied Sir John Norris into Connaught. Sir
Richard Bingham's disgrace had temporarily deprived the province of its governor, and he was appointed by his brother provisional president of Connaught, on Sir
Geoffrey Fenton's recommendation. The arrival shortly afterwards of the new president, Sir
Conyers Clifford, saw him return to Munster, and in June 1597 he had pacified it. On the death of Sir John Norris in that year he succeeded him on 20 September as
Lord President of Munster.
Thomas Burgh, 3rd Baron Burgh died also, and Norris was, on 29 October, elected by the council, as lord justice of Ireland. The election was not confirmed by Elizabeth, on the ground that his presence was specially required in Munster. Accordingly, Loftus and Gardiner having been appointed lords justices, Norris returned to Munster on 29 November. ==Later years and death==