The film's screenwriter Simon Pegg confirmed in an interview that her character is alive and well during the events of Star Trek Beyond, but that she's not on board the Enterprise. She's just...err...elsewhere.
“With this it felt like we would under-serve her if we included her,
she might end up feeling like she hadn’t been given the amount of
screen-time she deserves, so rather than bring her in and just have
her be a supporting role, like, have her not be in this one, and when
the time comes [bring her back], the worst thing to do would be to
have her in the film and have that character be killed, and that felt
like a cynical thing to do. We thought rather than have Carol Marcus
not be used to a reasonable capacity, let’s just not include her, have
her be alive, in canon, and ready to come back at any time.”
Remember Carol Marcus? Simon Pegg Explains Why the Alice Eve Character Wasn’t in Star Trek Beyond
So what was she doing?
The short answer is that she was off doing precisely what she was doing at this point in the prime timeline, developing the Genesis Project.
I think we had some lines to explain her absence in one of the initial
drafts that had her going off to start work on the Genesis project and
do sort of very, very early research on that. But it didn't make it
into the final cut.
Why Star Trek Beyond Didn’t Include Carol Marcus