What did Burke say about the social contract in Reflections on the Revolution in France or elsewhere, and how much did he develop his idea of a 'social contract for the ages'? How does this fit within the development of ideas about the social contract, and its applications in practice?
Consent and contract
One element in a contract is consent. Burke rejected consent as a basis for political authority and obligation :
The seventeenth and eighteenth centuries are commonly, and accurately, represented as the age of social contract theory: the time at which the still-popular doctrine arose that political legitimacy, political authority, and political obligations are derivative from the consent of those who create a government (sometimes a society), and/or who operate it through some form of quasi-consent (such as representation, majoritarianism, "tacit" consent, etc.) - that, in any case, legitimacy and duty depend on consent, on a voluntary individual act, or rather on a concatenation of voluntary individual acts, and not on patriarchy, theocracy, divine right, the natural superiority of one's "betters," the "naturalness" of political life, necessity, custom, convenience, psychological compulsion, or any other basis. It is not necessary to lay too much stress on this point with an American audience which knows that, according to the Declaration of Independence, governments derive their "just powers" from the consent of the governed; nor with an English audience familiar with Locke's Second Treatise. It does not, indeed, take much effort to show that, between the time of Hobbes in the middle of the seventeenth century, and that of Hegel in the early nineteenth century, consent emerged as the leading doctrine of political legitimacy, and that even writers such as Burke, who rejected consent and willing as the basis of authority and obligation, thought it useful to say that society was based on a metaphorical contract of some sort. (Patrick Riley, 'How Coherent is the Social Contract Tradition?', Journal of the History of Ideas, Vol. 34, No. 4 (Oct. - Dec., 1973), pp. 543-562 : 543.)
Burke : only a metaphorical contract
When Burke rejects consent as the basis of authority and obligation, he is not endorsing any kind of authoritarianism. Citizens have rights :
Far am I from denying in theory, full as far is my heart from withholding in practice . . . the real rights of man. In denying their false claims of right, I do not mean to injure those which are real, and are such that their pretend rights would totally destroy. ((E. Burke, Refections on the Revolution in France : online at https://archive.org/stream/reflectionsonthe005907mbp/reflectionsonthe005907mbp_djvu.txt.)
But the rights they have are not the natural or abstract universal rights of atomic individuals (the natural rights, droits de l'Homme, of the French revolutionaries or present-day human rights); they are the rights which citizens have as members of a historically specific society - a complex set of historically developed arrangements :
On Burke's view, society is an infinitely complex, historically developed system of customs; of habitual and reciprocal patterns of behaviors, prejudices, values, interests, and opinions - all apparently morally sanctioned - which are organically united so as to provide for the maximum satisfaction of interests. (Roger Paden, 'Reason and Tradition in Burke's Political Philosophy', History of Philosophy Quarterly, Vol. 5, No. 1 (Jan., 1988), pp. 63-77 : 66.)
In the England of his day this social complex included (Common Law) rights a fair trial, parliamentary government (but not universal suffrage), a form of the separation of powers (excluding arbitrary political intervention by the King), what would later be called the rule of law. He extended all these rights to the American colonists; they should not be taxed by a parliament in which they were not represented. Parliament had the legal power to tax the Americans without representation but exercise that power cut across the recognised rights of Englishmen which the American colonists were entitled to share.
Holding such views, Burke had no work for a social contract to do. He did not need it to uphold political authority and obligation since these were rooted in the arrangements of a historically specific society.
He talks of a social contract in a notable passage :
Society is indeed a contract. Subordinate contracts for objects of mere occasional interest may be dissolved at pleasure but the state ought not to be considered as nothing better than a partnership agreement in a trade of pepper and coffee, calico or tobacco, or some other such low concern, to be taken up for a little temporary interest, and to be dissolved by the fancy of the parties. It is to be looked on with other reverence; because it is not a partnership in things subservient only to the gross animal existence of a temporary and perishable nature. It is a partnership in all science; a partnership in all art; a partnership in every virtue, and in all perfection. As the ends of such a partnership cannot be obtained in many generations, it becomes a partnership not only between those who are living, but between those who are living, those who are dead, and those who are to be born. Each contract of each particular state is but a clause in the great primaeval contract of eternal society, linking the lower with the higher natures, connecting the visible and invisible world, according to a fixed compact sanctioned by the inviolable oath which holds all physical and all moral natures, each in their appointed place. (E. Burke, Refections on the Revolution in France : online at https://archive.org/stream/reflectionsonthe005907mbp/reflectionsonthe005907mbp_djvu.txt.)
This strikes me as an ironic retort upon social contract theorists. He is describing as a contract what is in fact no such thing. Rather, he is presenting a cosmology in which the human is connected to the divine, 'higher' to 'lower' natures, and the present to the future. It is an image of cosmic connectedness. One very obvious reason why Burke cannot have any literal contract in mind, explicit or tacit, is that it is impossible for there to be a contract between present generations and future : it takes two to make a contract, and future generations do not exist.