Hi Patrick,
The permission to "Add Entry" can be controlled via the permissions on each individual schedule.
1. As Admin, navigate to the Calendar tab
2. Select the lightning bolt next to the Schedule you'd like to modify, and select Edit
3. Select the Permissions tab
4. Create or modify a permission to grant 'Allow' for 'Can add entries.'
For example, if you'd like to grant Add access to the 'Scheduled Changes' schedule for Change Managers and Change Approvers groups, simply edit the existing permission for ServiceDesk.Calendars.Changes and grant 'Can add entries.'
I believe this permission was not granted to these groups by default because this schedule was designed to contain the entries automatically created during the Change process.
Good luck!