The New Event and Log Event button found on an entity record's Communication tab > Activities subtab is controlled by the permission named Events. To remove this button follow the steps below:
- Navigate to Setup > Users/Roles > Manage Roles
- Edit/Customize the role.
- Under Permissions subtab > Lists sublist, set the Events permission with Level = View.
- Click Add.
- Click Save.
Note: When we set the Event permission to Level = View, the role will also not be able to create new Event records when navigating to Activites > Scheduling > Events.