For a free-turbine (independent power turbine) engine only:
The prop speed, and thus the power turbine speed, is controlled by the prop governor. It modulates prop blade pitch angle to hold rpm.
At start of TO, the blade pitch is fairly low, but as you pick up speed, the rpm will tend to increase as inflow speeds up. (Fixed-pitch planes routinely experience this.) But the prop governor then feeds in a steeper blade angle to hold the selected rpm.
By the time you reach cruise, the blade tips would be supersonic -
so setting a lower prop rpm is in order.
Constant-speed props are preferred for aerobatics because the pilot doesn't have to monitor rpm; it remains constant whether going uphill or downhill.