Move cards only by the phase approver

I do not think that this is straight-forward possible. I can imagine a few workarounds though. Example workarounds:

1. 1. Have some sort of “password” field, that only the manager knows. Then, employ an automation: when this field has a different content, after the card has been moved to “approved” (or whatever your next phase is), move it back. Use a conditional to hide the field once it is filled in resp. when the current phase is the next one, so that other users cannot see the password. (NOTE: this is not very secure. Tech-savy users could find out the password).

2. 2. Have a required field: required fields can be used to prevent the move of the card. Problem is, that anyone who has permissions to edit fields can edit the required fields too. I could imagine using the connected cards (or database?) field here: then, set on the connected pipes (or database?) that only the manager can create/edit/access the connected pipe. This way, noone else should be able to edit/change the required field to a value that would allow the move of the card.
    
3. 3. Start with connected cards all together: have a separate approval pipe, which only the manager can access. Use the “All connected cards must be done before moving this card to the next phase” feature (see the screenshot below; together with the required connection field) in the pipe you have now to prohibit the move.