Good evening Ronald and welcome to the Events Calendar forum!
Thank you for your interest in our products and we’ll be glad to answer your question.
The short answer is yes. You can totally do that since Events are just like any other WordPress posts in many ways.
This means that you can make them private and even password protected out of the box.
Furthermore, if you want to have even more control over permissions and capabilities, you can do that using a plugin such as Members.
Finally, you could take this one step further and do template customizations to limit visibility of certain event categories to certain user roles.
That can be accomplished by reading our Themer’s guide.
Let me know if that helps.
Have a great day!
Geoff B.