The possibility of a Star Trek 4 definitely not looking good, first Anton Yelchin dying apparently killed momentum, and then the Marvel Movies raised the bar sky-high for what these kinds of movies need to make to ROI. Chris Pine, Chris Hemsworth being in and out of negotiations and ultimately backing away, just a big mess.
At this point it would probably be better to just reboot or move the movies up toward the TNG era and do Kelvin Next Generation. Hemsworth and Pine are big enough actors now that they will demand pretty big pay days and Trek movies really don't have the money making potential for it to be worth paying them several million dollars each.