Hi Ivan,
If you have set up the “Create items and edit items that were created by the user” option, to let certain users have the ability to edit other users’ item in Calendar List in SharePoint Online, you need to grant them the full control permission. You can stop inherited permission in the Calendar List and then grant those certain users with full control permission. This will only allow them to have this permission in the Calendar List and not the whole SharePoint site. About how to stop inherited permission and grant full control permission, see: Edit and manage permissions for a SharePoint list or library.
If you don't want them to edit the Calendar List settings, things will be a little complicated. You need first create a custom permission level in the SharePoint site and then grant this users with that permission level. To do so:
1.Go to the SharePoint site and then click Setting Gear> Site Settings> Site Permissions> Permission Levels> Add a Permission Level.
2.Type a name for this permission level and under “List Permissions”, select all permission except “Manage Lists - Create and delete lists, add or remove columns in a list, and add or remove public views of a list.”
3.Go to the Calendar List> CALENDAR tab> List Settings> Permission for this list> Stop Inheriting Permissions> Delete all the users and groups.
4.Click Grant Permissions and give normal users with Edit permission, then give those users who need to administer the list with the custom permission level we just created.
Regards
Fraser