King Daniel Into Darkness wrote:
Spock calls her "an additional science officer", so I assume she'll be part of his department. She's also a weapons' specialist, which will no doubt come in handy.
In the movie, it seems she took advantage of Spock being reassigned to get herself aboard the Enterprise. But then Kirk was allowed to retain Spock, and her orders were never changed. Had events not unfolded as they did, it probably would've been cleared up by moving Carol to another post on the Enterprise or assigning her to another ship.
As it is, she's on the five-year mission, and my guess is she'd defer to Spock as science officer and fall back on her expertise in weaponry to define her formal position on the ship. Since weapons are a part of security, that would mean changing into a red uniform, of course, God help her.