Internet security features continue to evolve and older versions of Safari cannot negotiate secure connections with newer sites.
If you are having trouble connecting to and using websites with your older version of Safari, try it with a newer third party browser that is still being updated to meet current internet security protocols.
I suggest you take a look at Firefox browser or Brave browser.
Your Mac may not support a newer macOS version so this will be your best option.
So that we can help you best, please tell us which Mac, model and year you’re having trouble with, and what macOS version you’re running. Find that info by clicking the Apple menu () at the top-left of your screen and then select About This Mac.