I've just searched for questions tagged star-trek-tng without being tagged star-trek. There are 79 of them, right now. (Here's where you can find them.) There also star-trek-tos, star-trek-voyager, and star-trek-ds9 questions without star-trek. Should we edit them? Do we actually need that tag on every single ST:TNG question?
After some discussion I'm fine with retagging all star-trek questions with the generic franchise tag. However, I would like it to be a coordinated effort during off peak (ie weekend evening) hours.
It would appear that you have already started changing them, without much discussion or allowing this meta question to receive votes.
There is no way to achieve this retagging automatically.
We could synonymise star-trek-tos, star-trek-tng, etc. with the master star-trek tag, but this wouldn't add the master tag to the old questions with the more specific tags, and it would mean no new questions would be able to have the specific tags.
Alternatively a moderator could merge the specific tags into the master tag, but that would mean losing the specific tags on all the old questions.
Neither of these outcomes is desirable.
The community appears to be against doing it manually.
As @JackBNimble suggested in his answer above, the manual retagging of all questions tagged star-trek-tng etc. without being tagged star-trek would be a massive undertaking which shouldn't be done bit by bit (messing up the front page for weeks or months) but in one coordinated effort.
And the response to this post was resoundingly against having another big manual tag cleanup effort any time soon. Most of those who responded or voted there felt that such a cleanup would cause more problems than it solved.
So it doesn't look as if this retagging is actually going to get done in the near future.
But we can still search easily for Star Trek questions!
One of the main purposes of tags is to aid searchability, and one of the main reasons it's undesirable for not all Star Trek questions to be tagged star-trek is that it makes it hard for people to easily find questions about Star Trek. But in fact we can search for all Star Trek questions, even with the tags in their current state!
[star-trek*] into the search box, and you'll get to this page, which lists every question with every.damn.tag that starts with the words "star-trek". The existence of this search ability eliminates a lot of the practical problems of not having a single unified Star Trek tag (even though I would still like very much to see every ST question tagged with star-trek).