Alice Eve’s character was revealed yesterday at Bad Robot Productions headquarters. After all the debates about what character Benedict Cumberbatch was to play, Alice Eve’s character has been overlooked. She will play Carol Marcus, Kirk’s former love (and mother to his son) from Star Trek II: The Wrath of Khan, played then by Bibi Besch.
Doctor Carol Marcus was one of the leading molecular biologists in the Federation. She devoted her life to her research.
During the late 2250s or early 2260s, Carol became involved with a young Starfleet officer named James T. Kirk, and in 2261 she gave birth to their son, David. However, she felt that they had no basis for a lasting relationship, with Kirk traveling around the universe while she worked in a lab, so she asked that Kirk leave her alone to raise the boy. That they both cared more for their careers than they did for each other was never disputed. As Carol saw it, she and Kirk lived in entirely different worlds, and she wanted her son to be raised in hers. – Source Memory Alpha
TrekMovie has confirmed that in Into Darkness she is a member of Starfleet and a science officer assigned to the USS Enterprise with the rank of lieutenant.