Okay. Because certain people seem to have trouble dealing with this concept:
- There is nothing in alpha canon that answers this question.
- I will therefore be resorting to beta canon (comics, novels) etc. to answer this question.
- Yes, I am aware they are not canon but they’re all we have.
All cool?
Okay.
There isn’t a huge amount on Gillian Taylor to be honest.
After arriving in 2286 she joins a Federation science vessel (which btw, aren’t they all science vessels?). Sources differ on the ship, it’s either the USS Clarke or USS Tombaugh.
The same year, she was also the first “patient” of the newly formed Department of Temporal Investigations.
She also seems to have remained as George and Gracie’s caregiver, and at one point needed Scotty’s help in treating them after they fell ill.
She also kept in touch with James Kirk and the two of them went on a month long ocean voyage together.
By 2287 she was dedicating her time to the New Cetacean Institute.
She attends Kirk’s funeral in 2293, and two years later publishes an autobiography/natural history book about whales.
And in 2310 she had moved to the planet Pacifica as part of an oceanographic study.
And that’s it. No tragic death. No abduction by Klingons. No getting assimilated by the Borg.
Gillian Taylor just had a normal happy life. Good for her.