A client recently asked: How do I restrict users from closing an Opportunity?
There is not a specific privilege for closing an Opportunity listed in the User Roles interface.
So instead you need to remove the “Append To” privilege from the opportunity for the role of those users who are not allowed to close opportunities.
Now when a user with that role tries to close an opportunity, they will get an “Insufficient Permission” error. Also, the user would not be able to add Activities to the Opportunity.