I wanted to give another department head access to be able to update the user profile service (specifically update Manager Field)? Is this possible or any other way to do it?
Due to limitations of SPO, only SharePoint Admin role can manage the UPA service. On-prem we have the option where we can add any user as administrator of the Service application.
check this Add and edit user profile properties
No. The user(s) must have the SharePoint Administrator role.