One of the biggest criticisms you can make about the Star Trek films is that it didn't really do much, if anything, to establish new characters. At least, establish them in meaningful ways. It's not something that's unique to any one version of the franchise. Arguably the character who has had the longest staying power is Carol Marcus and that's only because she appeared in two separate films, in two separate franchises (IE: timelines).
She wasn't featured in most movies, but she did jump through eras, something that hardly any of the characters have done. We're supposed to get Sybok at some point in Strange New Worlds' near future but as of right now, he's nothing more than a silhouette.
Yet, it didn't have to be this way. The Wrath of Khan, Star Trek's second film offering, really did a good job creating the baseline for Saavok, played at the time by Kirstie Alley. The character had an interesting foundation for a character, with her showing more emotion than most Vulcans. This has led to the idea that she was supposed to be a Romulan in hiding, or a half-Romulan, half-Vulcan.
That wasn't the only interesting idea, as she was supposedly set to be the mother to Spock's child. Though that idea too was dropped. Which is, in part, the issue. The character kept having major moments and elements eliminated from her character. Yes, they did move on from Alley, but Robin Curtis was always a better actress, so that shouldn't have been the reason why the character flopped in later films.
And she did, flop that is. Even in Star Trek III: The Search for Spock, Curtis' first, and Saavik's second, the character was already devoid of any uniqueness. It's like they were so mad at Alley for not returning that they nerfed the character out of spite. Yet, that wasn't the case, instead, Leonard Nimoy was the reason the character lost all of its zing from film to film.
It's a shame too. Saavik had a chance to establish herself as a major character in the Star Trek franchise beyond the two films. Yet, that's all she really did. They never went back to the well, and even by the sixth film, the character had been written out and forgotten about altogether. Replaced by a Vulcan character we never saw before or since in Valeris.
Imagine had we did. Imagine if Saavik was introduced in the second film as the half-Romulan, half-Vulcan she was meant to be. Who through five movies seduced and bore a child for Spock; only to betray him at the end. It would've made a marvelous five-film arc and would've given us a character to revisit in both the Kelvin Timeline and again in Strange New Worlds.
Yet, all Saavik is currently is a character who has a lot more to offer than she was ever really allowed to do.