This might be of interest as it also gets a bit of debate in forums from time to time:
Sturgeon wrote the screenplay for Amok Time. It was originally announced that T'Pau was going to be on Enterprise, but the Sturgeon Estate owns the character. This is the same reason T'Pau did not appear in the Yesteryear episode of the Animated Series.
It requires those running his estate to be sticklers, and generally speaking you kinda have to be a stickler if you're not going to see the estate be diminished by people taking advantage of it.
Harlan Ellison successfully sued Paramount in 2009 over use of material from City on the Edge of Forever in licensed novels (he sued for a 1$ plus expenses).
So yes, if you're going to use material which you don't own, you're going to have to negotiate with the owners over the worth of the material and while you're doing that any plans you have revolving around the material have to be put on hold and possibly won't come to fruition.
Now T'Pau is a relatively minor character in the original series but in ST:ENT she would have been a major, recurring character--second in command of the mission. It doesn't matter how minor she was in the episode, an estate would have to be insane or incredibly generous not to want a significant chunk of the profit from the use of the character. But let's be kind to the Sturgeon estate and say they may have been completely willing to be so generous. You still have that unless Paramount approaches them on the matter, they won't know and the easiest thing to do, because there is no inherent reason the tale of the first Enterprise has to have T'Pau as a character, is to simply choose another name for the character.
Nobody has said the Sturgeon estate were bastards. There may never have been negotiations over use of the character. But that does not mean that royalties to the Sturgeon estate were not a factor in the consideration of the naming of the character.
Source: https://forum.rpg.net/index.php?threads/wiw-star-trek-the-original-series.532768/page-30
The intention was for the Enterprise character T’Pol to be T’Pau, but that would have required paying a fee to Theodore Sturgeon’s estate for every use of the character.
Source: https://www.tor.com/2015/11/10/star-trek-the-original-series-rewatch-amok-time/
James Van Hise mentions Jerome Bixby and the Mirror Universe. In that situation, Bixby's loss had more to do with the way the Writers Guild of America (WGA) factored royalties--the Mirror Universe was a concept, not a character, and thus not something he could claim royalties for. On the flipside, Ted Sturgeon's estate would have received royalties for T'Pau had she been a regular character on Star Trek: Enterprise (as had been planned), which led the producers to simply rename the character T'Pol. Same character, different name, no royalty payments.
Source: https://www.peterdavid.net/archives/004740.html
Regarding legalities of character ownership and WGA contract specifics:
…freelance writers' contracts specify that royalties are owed if the guest characters are used in future episodes or movies. Up and till now, that didn't include their use in licensed tie-ins, but Harlan Elison has now decided to challenge previous interpretations in the courts.
T'Pau/T'Pol problem, where royalties were owed to the estate of freelance writer, Theodore Sturgeon.
Paramount owns the characters and can use them as they see fit. But they also have to pay the creators of the characters for their use. It's spelled out in the Writers Guild minimum basic agreement.
Source: https://www.trekbbs.com/threads/tom-paris-nick-locarno-question.99456/
Also of interest; but not answering the question:
Excerpt from "The Writing of 'Amok Time'
…delving into the Vulcan culture that nobody had ever seen before -- the ceremony, the formality, this woman who was head of the council, T’Pau -- that was all basically Sturgeon. But we made it more Star Trek.
Source: http://www.thesearethevoyagesbooks.com/the-writing-of-ldquoamok-timerdquo.html
And finally of interest is Theodore Sturgeon’s script copy for Gene Roddenberry.