His niece's husband, King Stephen of England, bribed David to obtain his support for his usurpation of the English throne. Wars with the Scots terminating in Stephen's victory at the Battle of the Standard occupied the early years of King Stephen's reign, 1135-1139.

From the book, "Scotland: a Concise History" revised edition, by Fitzroy Maclean, 1993, page 26:
On the death of his brother King Edgar in 1107, Alexander succeeded him. Alexander, however, only ruled over the land between Forth and Spey, leaving Argyll, Ross and even Moray to their own devices, while responsibility for Scotland south of the Forth was entrusted to his younger brother, David. In 1124 Alexander died and was succeeded by his brother, David, the 9th son of Malcolm III and already the ruler of most of southern Scotland.
page 27:
David, by a long way the most remarkable of Malcolm and Margaret's children, was to rule Scotland for close on 30 years. They were to be eventful years for Scotland. Like his brothers, David had been brought up in England, where he had received a Norman education and made many Norman friends and where, we learn from the patronizing William of Malmesbury, his manners 'were polished from the rust of Scottish barbarity.' In addition to being King of Scotland, he was in his own right Prince of Cumbria, and by his marriage to a rich Norman heiress, Earl of Northampton and Huntingdon. He was thus one of the most powerful barons in England as well as being the English King's brother-in-law.
On returning to Scotland, he proceeded to distribute large estates there amongst his Anglo-Norman friends and associates, such as de Bruce, Walter fitzAlan, a Breton who became his High Steward, de Bailleul, de Comines and many others, who thus became landowners on both sides of the Border. The Church, too, became the preserve of Norman prelates. Simultaneously David introduced into the Lowlands of Scotland something more closely resembling a feudal system of ownership, founded on a new, French-speaking Anglo-Norman aristocracy, who, although they intermarried and eventually merged with the old Celtic aristocracy, remained for a time separate and distinct from the
page 29:
. . . native population, many of whom still spoke Gaelic, save in the south and east where they spoke a primitive form of English. In the Highlands, meanwhile, a different, more patriarchal system prevailed and the King's writ counted for very little, while the Islands and parts of the mainland gave a loose allegiance to Norway.
In the course of his reign David sought to establish a national system of justice and administration under his own overall control. Alexander had already appointed a number of Court officials, such as Chamberlain, Constable, Chancellor, Steward and Marshal. From these and from the bishops David selected a central governing body to advise him, to carry out his commands and to deal with major administrative and judicial problems. He further appointed justiciars and sheriffs to administer justice. In the economic field he encouraged trade with foreign countries and established two royal mints and a standard system of weights and measures. He also granted the status of burgh to a number of towns, together with freedom from tolls, the right to hold markets and fairs, and also monopolies in respect of certain products. In order to keep in touch with his subjects, though also on sanitary grounds, he and his advisers moved constantly about the country from one royal castle to another.
Being a devout man, David also turned his attention to ecclesiastical matters, founding more bishoprics (under Anglo-Norman bishops) at Glasgow, Brechin, Dunblane, Caithness, Ross and Aberdeen, establishing more parishes, building more churches and endowing more monasteries, among them Kelso, Dryburgh and Melrose. But, while he accepted in general the universal claims of Rome, David wished the Scottish Church to retain a certain autonomy. Though ordered by Pope Innocent III, under threat of excommunication, to acknowledge the supremacy of the Archbishop of York, the Scottish Bishops, with the King's encouragement, rejected this proposition out of hand and so started a dispute which was to drag on for the remainder of the century.
page 30:
David's long reign was for the most part peaceful. In 1135, however, he chose to intervene in the dynastic disputes which developed in England, on the death of King Henry I, between his daughter Maud (Matilda) and her cousin Stephen. These he turned to his own advantage, successfully playing one side off against the other and, though defeated in 1138 at the Battle of the Standard near Northallerton, emerged, thanks to skillful negotiation, with precisely what he wanted, namely the greater part of Northumbria.
When David came to the throne in 1124, Scotland had, even by the standards of the day, been a primitive country with practically no towns and scarcely any industry or commerce. People lived in wooden houses and such trade as existed was conducted by barter. The different parts of the country were cut off from each other by barren stretches of uninhabited moorland and hill. It could hardly even be said that there was a common language. Latin, French, English and a number of Gaelic dialects were all spoken in different areas and by different classes of people. In the absence of any established feudal system, local chieftains felt free to disregard the authority of the King and of the central government. The Church, with only three bishops and no properly organized system of parishes, had very little influence one way or the other. When David died in 1153 much had changed. In the Lowlands, at any rate, what remained of the old Celtic way of life had been swept away and a new, relatively efficient, Anglo-Norman order of things established in its place. On David's death, the throne passed to his eldest grandson, Malcolm IV, a boy of 11.

Saint David established Norman law in Scotland, set up the office of chancellor, and began the feudal court. He also learned the spirit of Cistercian monks from Ailred of Rievaulx, who for a time was David's steward. Scottish monasticism began to flower from the start of David's reign and countless almshouses, leper-hospitals, and infirmaries were established. The monasteries founded under David's patronage were superb architecturally as well as spiritually. The king refounded Melrose Abbey on the main road from Edinburgh to the south, and it remained one of the richest houses in Scotland. David also founded Jedburgh Abbey in 1138, filling it with monks from Beauvais in France. At Dundrennan in Dumfries and Galloway he founded in 1142 a splendid abbey and staffed it with Cistercians from Rievaulx. The monks were so well managed that they even started their own shipping line and traded from the Solway Firth less than two miles away.