Hi Paul,
Welcome and thanks so much for reaching out!
It sounds like you may be interested in Community Events, which allows users to submit events to a community calendar.
With Community Events, if you go to Events Settings< Community, you can require Users to have a WordPress account in order to add an event:

You may also be interested in learning about and customizing Admin Roles and Permissions. You may want to install Members plugin in order to make this scenario work:
https://theeventscalendar.com/knowledgebase/admin-roles-and-permissions/
Please let me know how it goes and if you have any other questions on this topic!
Thanks,
Jaime