When you browse privately, the details of your browsing aren’t saved, and the websites you visit aren’t shared with your other Apple devices.
Browse privately on Safari
Choose Safari > Settings, and click General
Click Safari opens with, then choose A new private window
If this option does not appear, choose Apple menu > System Settings > Desktop & Dock, then turn on Close window when quitting an application
To stop browsing privately, open Safari > File > New Window to open a non-private window.