Hi,
Thanks for the interest in our plugins.
We do not have a way to make the calendar show only for registered users.
It could be possible with some customizations to do this.
You could follow our themer’s guide:
https://theeventscalendar.com/knowledgebase/themers-guide/
And modify the default event template to only show if someone is logged in.
This would work with the core version of the Events Calendar found for free on WordPress.org:
The Events Calendar
Beyond that we are limited in providing support on customizations.
Let me know if you have any follow up questions.
Thanks