So are they just going to ignore the events of Terminator Genisys?
Given it basically rewrote the original Terminator, everything thereafter is theoretically open to change. If Cameron and co. do want to keep continuity, Genisys, as shambolic as it was, is what should make it possible for Hamilton's Connor to still be alive post-1997.
Anyway, the Terminators have been crap since T2, so not holding out any hope here.
EDIT: Just remembered Sarah Connor Chronicles, which was pretty good, title aside. I liked Lena Headey as Sarah, too, even if she was quite different to Hamilton's original.