Let's not forget that before Cheers Kirstie Alley was the first (and best) Mr. Saavik!
Actually, Edward, they were actively developing a new TV series earlier, in 76/77. When Star Wars (not yet called "Episode IV") exploded on the scene and changed the movie industry, Parmount quickly rejiggered the in-preproduction series into Star Trek: The Motion Picture. (And there are still traces: for example, the new Vulcan science officer who was supposed to replace Spock in the series dies in the transporter accident early in the film.) When TMP was successful enough to spawn the film series, the TV idea was forgotten for a while.
The Next Generation was actually Gene Roddenberry's revenge after having been kicked upstairs to executive producer of the films... where he was no longer their guiding force, Harve Bennett and Nick Meyer were. Roddenberry wanted a Trek series that reflected the future the way HE envisioned it, though some of his main principles (like "no arguments between our lead characters, they are more evolved humans") had to fall by the wayside as he became ill and his control waned.
Eventually, Deep Space Nine was conceived by his successors as the anti-Roddenberry Trek, with a bunch of characters who aren't Starfleet's best and brightest, aren't on an exploration vessel, constantly disagree with one another, are enmeshed in a messy political struggle, display shades-of-gray morality, etc.