If you have started the Private time through DeskTime's icon in the system taskbar, DeskTime will stop tracking anything you do on your computer. To stop Private time, press the Private time option again. See how to enable Private time here.
When the Private time is enabled and active, then the desktop app's icon changes accordingly to the Private time icon:
Windows app:

Mac app:

Linux app:

This is how Private time would look on a Productivity bar:

Keep in mind:
You can disable the option of tracking Private time or the option to edit/delete the already tracked private time period in Settings → Account →Tracking:
- Uncheck Enable private time and the users will be restricted from tracking their private time. The option in their menu will be grayed out.
Uncheck Enable private time edits and the users won't be able to edit or delete their tracked private time.