Add role privileges of the custom post type

I wonder if it is possible when adding a new role add_role() I can assign to it a privileges to add, edit, delete posts of a custom type.

To be specific. I want to add a role 'volunteer coordinator' that can edit, add, delete events. Event is a custom post type.

The things that I managed to do is to assign privileges as a editor but this only works on the posts and the pages but not a custom posts events. I have a whole dedicated event section in the dashboard that I cannot see when logged as a volunteer coordinator. How can I make it visible, that volunteer coordinator can work with that section?

Or is there a way somewhere in the event plugin to make it visible for the new role?

Thank you