Because you are in the community, yes you can do this by adding a CSS override.
You can edit the community CSS overrides here:
You will then need to examine the html of the edit button, but it's going to be very similar to this:
<ul class="branding-actions slds-button-group oneActionsRibbon forceActionsContainer" >
<li class="slds-button slds-button--neutral slds-truncate" >
<a href="javascript:void(0);" title="New Event"
class="forceActionLink" role="button">
<div class="slds-truncate" title="New Event" >New Event</div>
</a></li>
</ul>
(Right click on the button and choose 'inspect' to see the html and css structure)
In the Edit CSS
area you will need to target the css + html structure of the button.
Something like this:
.branding-actions.slds-button-group.oneActionsRibbon.forceActionsContainer .forceActionLink[title="New Event"]{
display:none;
}
Hit save, publish the community and it should work.