Paramount has lined-up the next two installments for their Terminator trilogy, and are planing to put them into production very soon. Terminator 6 will be released on May 19th, 2017 and Terminator 7 will drop on June 29th, 2018. These dates are just markers for the studio, we've seen dates change all the time. However, this proves how serious Paramount is about finishing-up this trilogy.
The film rights to the Terminator franchise actually will expire in a couple of years. Once that time has been reached, they revert back to creator James Cameron. He's said once the rights return to him, he'll be axing the whole thing. I don't doubt this considering Cameron has zero plans currently to pursue more films, and is said to be focusing all his energy on multiple Avatar sequels (perhaps Battle Angel: Alita too). Paramount have a bit of a ticking-clock and have to grind-out these films before they can't make them anymore. Not the best situation for creativity, but let's see how Terminator: Genesys turns-out first.
Previous rumblings included that John Connor and the machines would actually have entire armies time travel, and have an epic battle across time. I assume these battles would be explored in the two sequels. We have no idea if Paramount is going to pursue this original intent for the trilogy, but the studio has seemingly gone-through with committing to three films, in a very short period of time.
It's assumed that Emilia Clarke, Jason Clarke and Arnold Schwarzenegger will be returning for the sequels. The fate of director Alan Taylor is a little less known, since he could move-on to other projects or asked to return for Thor 3 (very unlikely).
SOURCE: DEADLINE
