Edward Feser:

“It is the Burkean tradition – conservative, religious, celebrating deference and restraint and contemptuous of the “dust and powder of individuality” – to which Hayek points as providing both the true philosophical foundations of market society and the only hope of its renewal. Burke, along with Locke and the thinkers of the Scottish Enlightenment, represented in Hayek’s mind a “true individualism” which emphasizes ordered liberty and what the Catholic tradition would call subsidiarity, and has no truck with the radically autonomous self of contemporary egalitarian liberalism and popular libertarianism.”

I am not sure that I fully subscribe to this, but it would be an interesting project to explore strains in Burke’s thought compatible with libertarianism, understood as minarchist or anarcho-capitalist (a position that as it stands today I think an impossibility).