It may now be affirmed of civilized monarchies, what was formerly said in praise of republics alone, that they are a government of Laws, not of Men. They are found susceptible of order, method, and constancy, to a surprizing degree. Property is there secure; industry encouraged; the arts flourish; and the prince lives secure among his subjects, like a father among his children.--David Hume "Of Civil Liberty," (paragraph 12).
It will be found, if I mistake not, a true observation in politics, that the two extremes in government, liberty and slavery, commonly approach nearest to each other; and that, as you depart from the extremes, and mix a little of monarchy with liberty, the government becomes always the more free; and on the other hand, when you mix a little of liberty with monarchy, the yoke becomes always the more grievous and intolerable. In a government, such as that of France, which is absolute, and where law, custom, and religion concur, all of them, to make the people fully satisfied with their condition, the monarch cannot entertain any jealousy against his subjects, and therefore is apt to indulge them in great liberties both of speech and action. In a government altogether republican, such as that of Holland, where there is no magistrate so eminent as to give jealousy to the state, there is no danger in intrusting the magistrates with large discretionary powers; and though many advantages result from such powers, in preserving peace and order, yet they lay a considerable restraint on men’s actions, and make every private citizen pay a great respect to the government. Thus it seems evident, that thetwo extremes of absolute monarchy and of a republic, approach near to each other in some material circumstances. In the first, the magistrate has no jealousy of the people: in the second, the people have none of the magistrate: Which want of jealousy begets a mutual confidence and trust in both cases, and produces a species of liberty in monarchies, and of arbitrary power in republics.--David Hume "Of the Liberty of the Press," (Paragraph 2). [Emphasis added]
in a civilized monarchy, as well as in a republic, the people have security for the enjoyment of their property. David Hume "Of the Rise and Progress of the Arts and Sciences," (paragraph 29).
Philip Pettit likes to tell the story (it's a story of decline) how the modern, anti-Republican, account of ('negative') liberty can be traced (via John Lind) back to utilitarians like Bentham and Paley (see here). This account of liberty is the (quoting Bentham) "absence of restraint." (But recall, also, De Grouchy.) As Pettit notes, the consequence of this understanding of liberty is the decoupling of liberty from democracy. Equal absence(s) of restraint is possible, even actual, in democracies and (say) in monarchies.
Now, let's stipulate that Bentham is indeed the source of this (negative) new account of liberty. (Pettit notes that there are anticipations of the view in Hobbes.) But as the quoted paragraphs above show, Bentham's decoupling of liberty from democracy is itself a Humean move. The main point that Hume wishes to make is that freedom can (ought to?) be equated with the rule of law, that is secure property (recall the more expansive position in Adam Smith). That is a Republican trope, but then he he adds that some non-democracies, so-called civilized monarchies -- and he has great fun, of course, in treating Britain's great rival, France, as the exemplar of this -- can secure the rule of law as well as (republican) democracies. Hume's argument for this point turns on (perhaps optimistic evaluation of) how incentives are structured and are, thus, in part a contingent affair. (They are philosophically interesting because they make us look closely at institutional arrangements as a precondition of liberty.)
But here I want to close on another point of Hume's. He notes that in a monarchy, because the sovereign need not fear (or be anxious of) the citizenry, the rule of law generates "mutual confidence and trust" among the population and this is another species of liberty. Now, Hume does not say much about the nature of this liberty. But the (Humean) thought behind it seems fairly simple. The (proper functioning) rule of law reduces uncertainty and generates reliable expectations, even if one allows it may generate new kinds of uncertainty. (Its morality may itself rest on the normative umph of habituated, reliable expectations.) The thought then is that if the environment is stable and predictable, people are willing to plan ahead, and become more trusting and this is conducive to a kind of flourishing because we orient ourselves to others in a non-defensive manner. That is to say, in the right sort of circumstances we become better people: we are freed from suspicion and anxiety and this makes our actions more reasonable (driven by calm passions not violent ones).