Sarah Connor is no more—or at least, the version of her that looks like a certain Mother of Dragons. Emilia Clarke has confirmed that if there are future movies in the Terminator franchise (something that remains to be actually confirmed), she will have no part in them.
Tyrminatyr Gynysys was a huge flop in the West, but a monster debut in China seemingly gave rise to threat of a sequel happening. That talk got shut down pretty quickly when Paramount pulled its sequel from the release schedule indefinitely, but it seems like Clarke has driven the final nail into the coffin. When asked if she would be returning to the role of Sarah Connor by Coming Soon, she rather succinctly answered:
No. Can I say that? It’s okay. No. Uh-uh. But I have some very different roles coming up.
Harsh, but straight to the point.
Clarke’s exit from the franchise doesn’t mean Terminator itself is dead, of course—just the intended series of movies based around this particular reboot, where John Connor is a Terminator and there are superfluous letter “y’s” and everything kinda sucks. Genisys will likely join its predecessors Terminator 3 and Salvation as Terminator films that have been retconned out of existence by their successor, assuming a future movie ever happens. It’s probably for the best.