He was created Earl of Desmond 1329. Before that, he was Lord Of The Decies And Desmond from 1298 when his father died.

From "Complete Peerage England, Scotland, Ireland, Great Britian" by George E Cokayne, CS421.G2 1982, v IV, page 237, Desmond:
Morice fitz Thomas (a) brother and heir of his older brother, Thomas, was born 1293. On 5 Apr 1314 the King took his fealty and he had livery of his lands. (b) He was summoned for military service from 3 Apr 1322 15 Edw. II to 8 Dec 1322 16 Edw. II, by writs directed Mauricio filio Thome. He was present in a Parliament at Dublin, Easter 1324. (b) On 16 July 1327 he was admonished for refusing to obey the Justiciar. (b) Having quarreled with the Earl of Ulster, peace was made between them in a Parliament at Dublin in Mar 1329. (c) On 27 Aug. 1329 the King gave him all the royal liberties in county Kerry, except the four usual pleas and the profits from the crosses [churchlands] to hold, to him and the heirs male of his body, by the service of a knight's fee, by the name and honour of EARL OF DESMOND, and on this account the King girded him with the sword: (d) on the same day he was granted the advowson of the church of Dungarvan, that he might the better support the dignity of an Earl. (e) He was pardoned for all offenses committed in Ireland before 10 Oct, 14 Oct 1329. (f)
footnotes from page 237
(a) The arms of the Earls of Desmond were, Ermine, a saltire Gules. Crest, a boar Ermine, fretty Gules (or charged with a saltire Gules), armed and maned Or, and (sometimes) placed on a chapeau. Supporters, two male griffons Argent, their horns and rays [spikes] Or. Cry, "Shanet a boo" [Shanid, county Limerick].
(b) Patent Roll, 10 Edw. II, p. 2, m. 18: Close Roll [I.], 18 Edw. II, no. 12: Close roll, 1 Edw. III, p. 2, m. 21 d.
(c) On this occasion the Earl of Ulster gave a great feast in the Castle, Morice gave another next day in the Church of St. Patrick, and the Justiciar gave a third at Kilmainham. (Grace, Annales, p. 112.)
(d) "Edward. . .Come pur le bon et greable seruice qe nostre cher et foial monsire Morice filz Thomas Dirlande ad fait a noz progenitours et a nous et vncore fra a nous en temps auenir lui ecoms donez et grantez pur nous et pur noz heirs totes noz reales franchises qe nous auoms en Contez de Keri en nostre dite terre Dirlande forpris les quatre pledz cest a sauer forstal rap' tresor trouez et arzon et aussint les seruices des Croces en meisme le Contez a auer et tenir au dit Morice et a ses heirs madles de son corps engendrez de nous et de noz heirs par le seruice de vn fe de Cheualier sur noun et homur de Counte de Dessemond et sur ce li auoms ceint despe Et aussint eantz regard au seruice auantdit et qe le dit Morice se puisse de mielz contenir en lestat de Conte lui eoms pardonez pur nous et pur noz heirs a terme de sa vie la rente de deuz Centz marcs par an la quele rente est appellee la rente de Dongaruan. Ch. Privy Seals, I, file 164, no. 2879: also-without the last clause, which is on the Patent Roll, p. 2, m. 24-Charter Roll, 3 Edw. III, m. 15.
(e) Patent Roll, 3 Edw. III, p. 2, m. 24. This grant was revoked in Parliament, because it had been made by the advice of Roger de Mortimer, the King's enemy. Idem, 7 Edw. III, p. 2, m. 3.
(f) Patent Roll, 3 Edw. III, p. 2, m. 12. In 1329 he purchased, or pretended that he had purchased, from one Thomas de Carreu, who alleged himself to be kinsman and heir of Robert fitz Stephen, the over-lordship of the manors of Inchequin and Youghal, which manors were then held by Margaret, widow of Bartholomew de Badlesmere. Enrolments of deeds on Close Roll, 3 Edw. III, m. 13 d. But it was found by inquisition that the said Robert fitz Stephen-who tegether with Miles de Cogan had been enfoeffed by Henry II of all the desmesne of Desmond except the city of Cork-was a bastard and had died without children (Fine roll, 5 Edw. III, m. 4). It appears from a writ, dated 20 Jun 1342 16 Edw. III, that the Earl of Desmond then detained and occupied all the lands in Ireland of which Giles de Badlesmere (son of Margaret) had died seized, on the pretext that they were held of him, and not of the King. (Ch. Inq. p. m., Edw. III, file 57.)
page 238:
In 1330, he assisted the Justiciar, John Darcy, by subduing the O'Nolans and the O'Mores.(a) He was prohibited from attacking the Earl of Ulster, 19 Jun 1330: (b) both Earls were taken into custody, but Desmond escaped.(a) He was ordered, 28 Sep 1330, to appear before the King and Council, to receive justice in a certain matter (b) He absented himself from the Parliament held at Dublin in Jul 1331, but made peace with the Justiciar, Anthony de Lucy, at Kilkenny, on 5 Aug., and swore fealty to the King. (a) He was, however, arrested at Limerick, 16 Aug., and sent to Dublin Castle on 7 Oct. (a). Here he remained about 18 months, when, having found mainpernors, he was released. (a) On 16 Jul 1334, the royal liberties in county Kerry, which the King had resumed, were restored to him. (c) He was summoned for military service against the Scots, 8 May 1335, and accompanied the Justiciar, John Darcy, in his expedition to Arran and Bute in the autumn of that year. (d) The King's resumption of all grants made by himself or his father in Ireland, (e) and the removal from office of all Irishmen, and Englishmen who held no land in England, (e) having aroused much resentment, the Anglo-Irish lords absented themselves from a parliament summoned by the Deputy Justiciar, John Morice, in Oct 1341, and assembled at another convened by themselves at Kilkenny in Nov. (f) There they formulated their grievances and their charges against the King's officials. (g) The Earl of Desmond took a leading part in this affair. He summoned a Parliament at Callan on his own initiative in Feb 1344/5, but the magnates summoned failed to attend.
footnotes from page 238
(a) Annals of Ireland, pp;. 372-378: Clyn, p. 23.
(b) Close Roll, 4 Edw. III, mm. 29 d, 21 d.
(c) Patent Roll, 8 Edw. III, p. 1 m. 4. Grant ratified, 28 Nov 1336. (Idem, 10 Edw. III, p. 2, m. 13.
(d) Clyn, p. 26: Close Roll [I.], 9-10 Edw. III, no. 40. The year is usually given incorrectly as 1333.
(e) Fine Roll, 15 Edw. III, m. 14: Close Roll, p. 2, m. 28. The writs to the Justiciar are dated 24 and 27 July.
page 239:
He was summoned for military service in France, 10 Jul 1344. (a)
(f) Annals of Ireland, p. 383. Previous to this "numquam inter Anglicos in Agnlia oriundos et Anglicos in terra Hibernie oriundos ita notabilis et manifesta divisio habebatur.
(g) The petitions and the King's answers are on the Close Roll, 16 Edw. III, p. 1, mn. 25 d, 24 d.

Desmond had the wardship of the 2d Earl of Ormond during Ormond's minority. Desmond got into trouble with the Lord Justice d'Ufford; he was forced to surrender on bail on the recognisances of the Earl of Ulster, the Earl of Ormond, and 24 knights. But d'Ufford being a severe man, Desmond did not appear. The bails were estreated with the exception of the Earl of Ormond who was a minor and a ward of Desmond, the Earl of Ulster and two others. In consequence of Desmond, who was the ruler of a Palatinate in Kerry, using his power to resist the royal authority, King Edward III, by Letters Patent, granted to Sir John Darcy, Lord Justice, in consideration of his good services and the sum of £1,000 the marriage of James le Botiller, Earl of Ormond, now in his minority. He also granted him the custody of all the lands of the late Earl of Ormond held in capite during the minority of his son.29