While Star Trek Beyond wisely kept all of the main Enterprise crew intact, that doesn't mean every important character from the reboot series returned. One notable absentee from the third installment was Alice Eve's Carol Marcus. Despite joining the crew at the end of Star Trek Into Darkness, Carol was nowhere to be seen when the ship had its conflict with Krall. According to Simon Pegg, the reason for her absence was because they didn't have any decent material for her.
Rather than throw Carol Marcus in and not have her do anything important, Pegg explained during his appearance on Engage: The Official Star Trek Podcast that they left her out of Star Trek Beyond so they could save her for something meaningful the future. As he put it:
We thought rather than have Carol Marcus be not used to a reasonable capacity, let's just not include her, have her be alive, in canon, and be ready to come back at any time.
Alice Eve's Carol Marcus was originally introduced as Carol Wallace early on in Star Trek Into Darkness, telling Captain Kirk and Spock that Admiral Alexander Marcus had assigned her to the Enterprise. However, her true identity was eventually revealed, and she explained that she had come on board to investigate the proton torpedoes her father had ordered Kirk to bring onto the Enterprise. The crew soon learned that those torpedoes were actually stasis chambers containing Khan Noonien Singh's men. Carol was later injured aboard USS Vengeance and watched Khan kill her father, and a year after the superhuman was defeated, she officially joined the Enterprise as a science officer.
Now that we know why the writers opted not to include Carol Marcus in Star Trek Beyond and that she's alive out there, that brings up another question: where exactly was she during the recent events? It wasn't said in the movie, but Simon Pegg revealed that there was dialogue from one of the script's drafts suggesting she was going down the same path as her original timeline's self (played by Bibi Besch) in Star Trek II: The Wrath of Khan. Pegg continued:
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.
For those who haven't seen Star Trek II: Wrath of Khan, Project Genesis was intended to take uninhabitable planets and transform them into suitable habitats for humanoid life. Not only was the Genesis device a key plot element in Wrath of Khan, but its effects also factored heavily into The Search for Spock. Assuming those lines from the Star Trek Beyond draft are canon, it appears the starship life wasn't for Carol, and at some point before the third movie kicked off, she departed to work on this timeline's version of that experiment.
You can see Star Trek Beyond in theaters now, and with Star Trek 4 already in the works, maybe we'll hear news in the near future about Alice Eve reprising her role.