When Nero and his Romulan crew traveled back in time at the beginning of the 2009 Star Trek reboot, it kicked off a series of events that would distinguish this reality as the Kelvin timeline. Among the differences in this timeline is that rather than live to see his son become captain of the Enterprise, George Kirk died minutes after James Tiberius Kirk was born, leaving James' mother, Winona, to celebrate James' birth and mourn her husband's death at the same time. As far as we know, Winona Kirk is still alive as her son and the Enterprise crew explore strange new worlds and all that jazz, and with Star Trek 4 in the works, Jennifer Morrison is game to reprise her role in the upcoming movie. When asked if she was interested in joining the project, she responded:
I would love that! I don't have any idea what they are doing. I have not heard from anyone. So, I don't know where they are in the process. I don't even know if they have a script. I have no idea where they are at with all of it. But, I loved being a part of that franchise. I loved playing Winona Kirk. I feel super honored to have played Winona Kirk. And any way to be possibly involved, I would of course love to be.
Given that Jennifer Morrison didn't show up in either Star Trek Into Darkness or Star Trek Beyond, one might wonder why she'd stand a better chance of showing up in Star Trek 4. For one thing, those other movies coincided with her time on the ABC series Once Upon a Time, and now that the show has concluded, presumably the actress' schedule isn't quite as packed, allowing her to possibly participate in Star Trek 4. More importantly, though, is that back when Star Trek 4 was first announced two years ago, it was said that the story would involve James Kirk crossing paths with his father, reprised by Chris Hemsworth. It's unclear if this is still the narrative plan, but if it is, that potentially paves the way to include Winona Kirk as well, whether it's her present day self or a past version of her.
As Jennifer Morrison stated during her recent appearance at Montreal Comic-Con (via FTWwsWTF), she's on board to appear in Star Trek 4 if asked, but for now, she remains in the dark on what's happening. In fact, aside from the main actors all reprising their roles (with the exception of the late Anton Yelchin), all we know for certain about Star Trek 4 are that S.J. Clarkson is directing it (making her the first woman to direct a Star Trek movie), J.D. Payne and Patrick McKay are writing the script, and J.J. Abrams and Lindsey Weber are producing. This is one of two Star Trek movies currently in development, the other being the Quentin Tarantino-pitched project that's being written by Mark L. Smith and might also star the rebooted Enterprise crew.