I've been watching Brantley a little. I think he projects as a back-up big who brings a physical presence and energy off the bench. He needs to slim down to around 245 lbs and work on his defense, getting in a stance and moving his feet better. Whether he's able to get on the floor and stay there will likely depend on his ability to knock down shots from NBA range, something he's shown flashes of, but remains to be seen. If things go well, I could see him have a role similar to Montrezl Harrell who came into the league as a similar energy-type player and took a couple years to get consistent minutes. Harrell is an inch taller, 2 inches longer and more vertically explosive than Brantley, but Brantley is much more skilled with the ball as a handler and passer, and is a much more promising shooter.
It's likely going to be a year or two before he gets real minutes with the Jazz. Expect to see him with the Stars this year.