I think that Conservatism is an inherent view of the world that the social order is pretty good and should be preserved. It is a reverence to the great institutions of modern life – business, religious, and government.
Should anything need to be changed, it should be done in small, carefully considered steps so as not to damage what we already have. Large, drastic changes are to be avoided because the consequences may disrupt the social order.
Many people think that the issues a Conservative supports defines Conservatism, but they cannot be more wrong. Conservatives support these issues because of their Conservative view of the world.
Radicals want to make big changes and take great chances in changing the social order. Whether these radicals are on the left or the right or somewhere else, they are still radicals and anti-Conservative. The goal of radicals is to tear down what we have and build something else to replace it with the notion that the world is so evil whatever they come up with to replace the social order has got to be far better than what we have. This is rightly seen by Conservatives as being very dangerous to the world order.
Progressivism, Communism/Socialism/Marcism, and Trumpism are all radical. There is nothing Conservative about any of these.
Initially, Capitalism was very radical because it threatened to shake the social order and it did just that. Instead of advancing to the upper echelons based on your family connections, it became more and more possible to advance because of your ideas and hard work. Over time, Conservatism has seen more and more the advantages of Capitalism and have somewhat taken it in, but with some reservations. You might say that Conservatives often favor Capitalism as long as it is under their control.
Classical Liberalism is based on Capitalism beyond what Conservatives feel comfortable with largely because Classical Liberals see greater value in Capitalism and want to extend it beyond what most Conservatives would be comfortable with doing. In general, though, I think that Classical Liberalism and Conservatism are fairly compatible with each other. It would be great if Conservatives would be more receptive to Classical Liberalism.
I often describe Libertarianism as “Classical Liberalism taken to extremes”. It is more radical, I think, than Classical Liberalism itself, but at least Classical Liberalism is generally at the heart of Libertarianism.
Note, however, that there are some factions of Libertarianism that concentrates more on the freedom expressed by Libertarianism rather than the Classical Liberalism at the heart of Libertarianism.
Anyway, Libertarianism is not Conservatism, but they do intersect in some ways.
So that’s my opinion of how they are related.