All Cal.com users have the ability to create private events. The only difference between a private event and a regular event is that a private event isn't going to be displayed on your public profile. All events can easily be switched from public to private by accessing them on your event type page.
You'll notice that each event has a toggle towards the right-hand side of the screen. Activating or deactivating this toggle switches the event between public and private modes. Once you've switched an event to private mode, people can still book that event; however, they would need to have the direct link as they won't be able to see the event on your public profile.