Sometimes considered 2d Earl of Ulster

From Concise Dictionary of National Biography, DA28.D55 1939, p169:
Richard de Burgh, 2d Earl of Ulster and 4th Earl of Connaught 1259-1326, eldest son of Walter De Burgh, Earl of Ulster, (q.v.) succeeded to earldom 1271; made war on his late guardian, 1282; ravaged Connaught, 1286; deposed Brian O'Neill and made Niall Culanach O'Neill King of Ireland, 1286; ceded Isle of Man to Edward I, 1290; conquered Magres O'Connor of Connaught, 1292; summoned by Edward to serve in France, 1294; imprisoned by FitzGerald, his feudal enemy, 1294-95; made Aedh O'Connor Chief in Connaught, 1296; joined Edward I in Scotland, 1296; summoned to serve in France, 1297; served in Scotland, 1304; built Sligo Castle 1310; at war with other Irish nobles, 1311; made Felim O'Connor Chief in Connaught, 1315; fought against Edward Bruce, 1315; imprisoned at Dublin, 1317 in order that he might not join his son-in-law, Robert Bruce; frequently summoned to serve with Edward II in Scotland till 1322.

From "A New History of Ireland", vol IX, p170:
He was 3rd Earl Of Ulster from 1271-1326.

In 1295 the king summoned the great men of the kingdom to attend him in his invasion of Scotland, including Theobald le Botiller, the Lord Justice, Richard de Burgo, Earl of Ulster, and others. They went thither early in the spring and were nobly entertained by the king on Whitsunday, May 13th, 1296, at a solemn feast in the Castle of Roxburgh.94

1313 Edward Bruce, brother of the KIng of Scots, invaded Ulster with a great army in May. He burnt Dundalk, defeated the Earl of Ulster, and took the Castle of Norburgh. After this Bruce proceeded to Finnagh and the Skerries in Leinster, where he encountered Edmund Butler, Lord Justice of Ireland, Richard the Red Earl of Ulster --"and every one of them had a great army to war against Bruce. And upon a sudden there arose a great dissension among them; and so they left the field, and this dissension happened on the 26th day of January." Bruce returned to Ireland before Easter with the Earl of Murray and an army; they proceeded to Castleknock, where they took the Baron Hugh Tyrell prisoner. After a short rest Bruce went to Limerick and stayed there until after Easter. Roger Mortimer, the King's Lieutenant, landed in Waterford with a great army in 1316 and Bruce retired into Ulster. Also there was a great slaughter made by Edmund Butler near Castledermot upon the Irish, and another slaughter by the same Edmund upon Omorthe and Balitcham. In 1317 King Robert Bruce came to assist his brother Edward with an army of 20,000 men. They marched to Castleknock. Bruce marched to Limerick and from thence to Castleconnell, Cashel, and Nenagh, laying waste with fire and sword the English settlements through which he passed. Bruce laid waste the lands of Edmund Butler in the counties of Kilkenny and Tipperary, but not the Castle of Nenagh. Thomas FitzGerald of Kildare, Richard de Clare, Arnold Power, the Lord of Dunoyle in Waterford and others took the field against Bruce, but they were afraid to attack him. Robert Bruce returned to Scotland, leaving his brother Edward to carry on the war. During this year so great a family prevailed that cannibalism was reported. In 1318 a god harvest enabled the armies to take the field again--Edward Bruce had about 3,000 men. The English were led by John Birmingham. The last battle took place at Faughard on 14 OCt 1318. John Maupas, an English knight, slew Bruce. Birmingham sent the head of Bruce to King Edward II who rewarded him by making him Earl of Louth. In this war Edmund, Earl of Carrick, and his knights played a prominent part; it was for that reason Bruce devastated the lands of Butler. 94

Fought at Bannockburn for the English King against his son-in-law Robert the Bruce.9

Richard Og de Burgh, 2nd earl of Ulster, the Red Earl. (1259 – July 29, 1326) was one of the most powerful Irish nobles of the late 13th and early 14th centuries, a son of Walter de Burgh, the 1st Earl of Ulster (of the second creation) and Lord of Connacht.[1] His name, "Richard Og" meant Richard the Young, probably a reference to his youth when he became earl in 1271, or to differentiate him from his grandfather, Richard Mor. He was also known as the Red Earl.
Richard Og was the most powerful of the de Burgh Earls of Ulster, succeeding his father in Ulster and Connacht upon reaching his majority in 1280.[1] He was a friend of King Edward I of England, and ranked first among the Earls of Ireland. Richard's wife Marguerite de Guines was the cousin of King Edward's queen. He pursued expansionist policies that often left him at odds with fellow Anglo-Irish lords.
He led his forces from Ireland to support England's King Edward I in his Scottish campaigns and when the forces of Edward Bruce invaded Ulster in 1315, the Earl led a force against him, but was beaten at Connor in Antrim. The invasion of Bruce and the uprising of Felim O'Connor in Connacht left him virtually without authority in his lands, but O'Connor was killed in 1316 at the Second Battle of Athenry, and he was able to recover Ulster after the defeat of Bruce at Faughart.[1]
He died July 29, 1326 at Athassel Priory, near Cashel, County Tipperary.