In addition to the first look at Terminator Genisys in the form of the magazine covers, official plot details are let loose about Emilia Clarke's character, Sarah Connor.
Here's the relevant info via EW:
Sarah Connor isn’t the innocent she was when Linda Hamilton first sported feathered hair and acid-washed jeans in the role. Nor is she Hamilton’s steely zero body-fat warrior in 1991’s T2. Rather, the mother of humanity’s messiah was orphaned by a Terminator at age 9. Since then, she’s been raised by (brace yourself) Schwarzenegger’s Terminator—an older T-800 she calls “Pops”—who is programmed to guard rather than to kill. As a result, Sarah is a highly trained antisocial recluse who’s great with a sniper rifle but not so skilled at the nuances of human emotion.
Since she was 9 years old, she has been told everything that was supposed to happen. But Sarah fundamentally rejects that destiny. She says, ‘That’s not what I want to do.’ It’s her decision that drives the story in a very different direction.
Terminator Genisys has a July 1, 2015 release also starring Arnold Schwarzenegger, Jai Courtney, Matt Smith, Jason Clarke and J.K. Simmons.