Terminator Genisys ended with Sarah Connor, Kyle Reese and the older-looking T-800 (“Pops”) driving off into the sunset to take part in another mission to prevent the rise of Skynet, but the second film would’ve shifted focus to give us more backstory on the villain’s arc.
Specifically, it looks like the second film would’ve explained how John became a Terminator-human hybrid.
So if you walked away from Terminator Genisys scratching your head about the fate of Jason Clarke’s John Connor, then it sounds like the later installments in the proposed trilogy would’ve fleshed out that narrative in more detail.