We cannot add a button in the header, footer, or sidebar as that is all controlled by the theme. So we do not add a link around the calendar as instead of asking why there is a link there people would be asking us how to remove it.
There are many options to adding links:
You can in the Event Settings add html before or after the Event Content so that is one place to add a link.
You can add a link in your theme using the Menu Editor as a custom link.
Or you could follow our themer’s guide and add a link in any event template:
https://theeventscalendar.com/knowledgebase/themers-guide/
The link to add events for Community Events defaults to:
yoursite.com/events/community/add
And to mange events there is this link:
yoursite.com/events/community/list
Cheers