1. The Starting Lineup
Last season, Kanter spent almost all of his time at the center spot, backing up Steven Adams. And until the playoffs against the Spurs, the Thunder rarely used the jumbo Adams/Kanter lineup. But with Ibaka being traded, the power forward spot is much thinner than last year. Ersan Ilyasova will soak up some of Ibaka's minutes, but other than him, the Thunder don't really have any other true 4s on the roster. And Kanter is almost certainly the best of the hybrid bigs (Mitch McGary, Nick Collison, and Domantas Sabonis are the others) which means Kanter should get a lot more playing time.
2. After Westbrook, Kanter is there?
Durant leaving the team should leave a massive hole in the area of scoring. And Kanter is the most likely one to step into the void. (At least, what is left after Westbrook is finished) Kanter is probably the team's 2nd best scorer at this point, and so he will be asked to do a lot more creation on his own and will almost certainly be the featured offensive player for any minutes that Westbrook is not on the floor.
3. The Stretch Power Forward
Another thing that the Thunder lost with Durant and Ibaka was a lot of shooting, and the spacing it provides. This will likely mean that Kanter will be asked to stretch his own game a bit more out to the 3 point line, (particularly if he spends significant time at the 4 spot as mentioned above.) and while he has never shot a lot from that distance, he has proven a good shooter at this point in his career, and there is good reason to believe he will be at least decent from deep.
4. The Spacing
To piggy back onto the last point, the Thunder will have issues with spacing this season. Particularly since their new SG (Oladipo) is not a great shooter, and Andre Roberson (a total non-shooter) is likely to have a much higher minutes total. As such, having a post up guy who can bully through traffic to get buckets will be even more valuable. Kanter is exactly that sort of player, as such, he should be heavily featured even when Westbrook is on the floor because Kanter's scoring will not be as effected by the lack of spacing.
5. The Prime Time
Kanter is not 24 years old. Generally, that is the age where players end up really filling out into their top form and their prime begins. Combine all of the situational reasoning from above with the fact that he is about to enter his real prime, and Kanter should be looking at a career season for the Thunder. The only question about him this season should be about his defense, which he also did make (small) strides in improving last season.