The Calendars and Contacts plugin is installed in WHM » Plugins, however the Calendars and Contacts icon does not show in cPanel » Mail when enabled in the Feature Manager.
The Calendars and Contacts plugin uses the cpdavd service to process and maintain system calendars. If this service is disabled, the icon will not be shown within cPanel accounts.
The configuration can be verified by visiting the Calendars and Contacts URL such as the following:
Ensure that the cPanel DAV Daemon service is enabled (and monitored) in WHM »Service Configuration »Service Manager.