You are referring to a Vicarius (as in vice-president or vice-roy. Latin- vicis- an interchange). He was a bureaucrat who carried out the actual day to day administrative tasks for an elected official. Eg- vicarius praetoris-- "in the place of the praetor."
Well positioned slaves, like maybe a personal tutor or valet might have slaves to meet his needs- vicarius servi.
https://en.wikipedia.org/wiki/Vicarius