(written from a Production point of view)
According to the script for Star Trek II: The Wrath of Khan, the Starfleet General Staff was a group in Starfleet Command. Members of this staff had access to information about classified projects, for example, Project Genesis. In March 2285, Rear Admiral James T. Kirk was on this staff. This group was not referenced in the theatrical, but was in the director's cut of the film.