GKT is just an ordinary drill, and you level it up as any other drill. It doesn't goes up automatically every time you tap Defense and choose to improve another defensive drill. All I want to say is if you have high level GKT, you can virtually improve level of any other (low-level) drill by adding several GKTs before that drill in the training schedule.
It is good to have GKT as high level as possible. It is also good to have all the drills unlocked. But it's not that important to level up other drills after you have unlocked them. Levels in GKT are more useful.