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 & Subscribers > Invite 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.