"Move all subtasks" is not a native Jira function, so I suspect you had an add-on providing it.
I'm sorry, but I can't find an add-on that might do it in the marketplace, so I think I'd want to ask your admins what was providing it before.
To set up "Move" you must browse the permission scheme:
Ability to move issues between projects or between workflows of the same project (if applicable). Note the user can only move issues to a project he or she has the create permission for.
--> Subtask -> Move to another Parent Issue
Hope this will be helpful!
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