You can set up your calendar to show when your schedule or a team member's schedule is Busy or Unavailable.  Event titles will display as "Busy" or "Unavailable" for anyone that's not allowed to edit those events.

1) Set up Busy Option:
 

Login as Administrator >  Admin Menu > Calendar Options  > Advanced Tab > under "Show Events As Busy" section >
Select  "Show event title as busy if user not allowed to edit event" > Customize the "Busy" text.  Other popular options would be "Unavailable" or "Booked" > Save
 

2) Set up Self Service Booking (Optional):

The Busy feature can be used in conjunction with category options to set up a private, Self Service Booking Calendar in which you prevent double booking of a schedule.

Go to Admin Menu > Categories > Select category you want to allow others to "Self Book"  > Edit >  check D. Self Booking  and F. & G .Prevent Double Booking of events in this category > Save

Next, create a basic user account for each person allowed to add events via:

Admin Menu > Users & SubscribersInvite User

Do not give category manager or administrator editing permission to these users otherwise they will be able to see all events. The set up described will allow a user to login and add / edit events in a category but only view the 'Busy' text for other events.