The current version of PT4 (v4.15.25) should run on Big Sur - we have been testing on the beta version for a while and I haven't seen anyone else reporting problems yet.
If you're not using 4.15.25 you can download it from the
PT4 Download Page.
If you continue to have problems after that please follow the directions in the
Tutorial: Reporting a problem to start PT4 with logging enabled and send us a log file if one was created, so that we can see what is going on in your case.