There were never any plans for a TV movie or mini-series to span the gap between the two films.
As I said earlier, there was no perceived "gap" when ST II was being filmed, but it was originally conceived as a telemovie
(to be released theatrically overseas), as were films like "Buck Rogers in the 25th Century", "Duel", "Battlestar Galactica" and "Mission Galactica: The Cylon Attack".
And Kirstie Alley and Merritt Butrick were groomed as the featured players for a potential
series of telemovies, had Shatner and Nimoy continued to be disinterested in future Treks on TV.
A previous thread: