That is the topic of my latest Bloomberg column. I suggest it will take three major forms, namely anti-China, pro-internet as a communications medium (as an offset to left-wing media), and dislike of the Left, most of all the latter. Note these are predictions rather than normative claims about what should happen. Here is one excerpt:
Last and perhaps most significant, the intellectual right will dislike the left. It pretty much does already, but the antagonism will grow. Opposition to political correctness and cancel culture, at least in their left-wing versions, will become the most important defining view. As my colleague Bryan Caplan succinctly put it four years ago: “Leftists are anti-market. … Rightists are anti-leftist.”
The intensity of this dislike will mean that, within right-wing circles, free speech will prosper. As long as you take care to signal your dislike of the left, you will be allowed to hold many other heterodox views without being purged or penalized.
If you are on the Left, note that it does not suffice to dislike the Right, you have to dislike most parts of the Left as well (why is that? Can you model this?).
I also consider social conservatism, libertarianism, communitarianism, and Sam’s Club Republicanism as possible alternative directions for the intellectual Right. The entire column repays careful study.