Yes correct tyre pressure may help .
I run 2.2 and 2.4 bar on my tre1130 k yours may be different.
Good tyres and well set up suspension are key for the best handling on any bike .
However I would be looking at checking wheel bearings and steering head bearings as well, just to eliminate them.
The main thing you need to do is to get the suspension setup for your weight first.
I'm not familiar with this models suspension settings but it must at least have preload on the rear shock to help get the correct sag level.
Also the front forks may of been lowered or risen in the triple clamps by the previous owner.
Again a suspension guru will help you with these issues .