Restrict Clearing Website History

Yes, create a configuration profile and enable the Content Filter payload.
Turning on any of the basic filtering settings will remove the option for Private Browsing altogether. 
Also the ‘clear all’ button is disabled in History and prevents removal of any sites. 
These settings for Safari work the same across iOS and macOS, both work well in our environment.

You can do the same restrictions for Chrome on macOS although not iOS. Because of this we removed Chrome on our iPads and use only Safari .

Hope that helps

Assuming you use Google Workspace and managed Google accounts, you'll want to take a look here to manage a user's Google Chrome usage. If you take a look at the third setup step, there is a very long list of things you can manage in Google Chrome, including whether the user can use Incognito Mode or clear their browsing history.

This is something we'll be diving into once we catch up on our other projects, so I don't know the process myself yet. This thread may help you start in the right place, at least.

Hi,

but it isn't possible to activated Web content Filter but allow safari history? Why was not separated?

Is it an topic for Jamf Feature Request? 

Best regards

Peter

That should be filing feedback to Apple, not a Jamf request. It is the way Apple designed it.