Browse privately one time
In the Safari app on your Mac, choose File > New Private Window, or switch to a private window that’s already open. A private window has a dark Smart Search field with white text.
Always browse privately
In the Safari app on your Mac, choose Safari > Settings, then click General.
Click the “Safari opens with” pop-up menu, then choose “A new private window.”
If you don’t see this option, choose Apple menu > System Settings, click Desktop & Dock in the sidebar, then turn on “Close windows when quitting an app” on the right. (You may need to scroll down.)
For more info, click on this link here: Browse privately in Safari on Mac