For Kyrie to take that 'next leap' he's going to have to realize a jump in numbers, either scoring more per game or in assisting more per game or both.
In order to score more, he'll have to either take more shots or shoot more efficiently (or both).
He already was 6th in the NBA in FGA/game. He was the highest USG player in CLE and took the most shots there. He also took just slightly more FGA/game than Isaiah took here and the identical FGA/possession as IT (even though the latter was pretty much the only real offensive weapon here last year). I don't know if it is reasonable for us to expect Kyrie to take more shots this year than Isaiah took last year, when we've added another elite scorer like Hayward who should be getting far more shots than say, Avery did last year. I mean, if Hayward isn't taking more shots per possession than Avery took last year, then something is broken in our offense. So I'm just not seeing a lot of room for more shots for Kyrie to take.
So in order for him to score more points, it really has to come from improvements in efficiency. So the question is: Can he score more efficiently in this offense, playing off Hayward & Horford than he did in CLE, playing off Lebron and Love?
As far as assists go, again, the question is one of touches. Brad's offense relies heavily on passes from front-court facilitators. He's made a point of running his offense through 'point forwards' like Sully, Evan Turner, Kelly Olynyk and of course, Al Horford. Last year especially, down the stretch the offense was more and more effectively run through Horford's capable hands. Isaiah played a LOT off the ball because of Al's great passing skills and I don't see why Kyrie wouldn't continue to do that as well. And we've added another great passing forward in Gordon Hayward.
Kyrie's touch and passing rates were not really very different from Isaiah's last year. I was fully expecting Thomas' touches (and passes and shots) to all go down slightly with the addition of Hayward. I don't see why we should expect Kyrie's to go up much.
So, basically, the only realistic avenue for dramatic improvement in Kyrie's game has to be through improved scoring efficiency. He has to elevate his TS% from the .560-.580 level that it has been through most of his career up closer to or above the .600 level where the MVP candidates like Curry, Harden (and last year at least, Thomas) play. He's got to change his shot profile.
He's got to do that by taking fewer mid-range 2PT shots. He basically needs to 'be like Thomas' and drive more (getting to the FT line more) and take more 3PT shots. He has the ability to do both those things more. So this is not an unreasonable hope.