Assistant director was a leadership position that ranked below that of a director.
In 1986, Doctor Gillian Taylor was the assistant director of the Cetacean Institute. (Star Trek IV: The Voyage Home)
In 2375, Luther Sloan introduced himself to Admiral William Ross and Senator Kimara Cretak as "Wendell Greer, Assistant Director, UFP Department of Cartography." (DS9: "Inter Arma Enim Silent Leges")