For most light aircraft the prop will remain on the fine pitch (high RPM) stops
untill it reaches 70 to 100 knots on the takeoff run. At that time the prop will start to unload and speed up, so the govenor will increase the pitch of the prop blades to stop the prop from speeding up and exceeding the seelcted RPM (Redline in the case of the takeoff)
If there was a failure which caused the prop togo to the fine pitch stops during cruise flight the prop will very significantly exceed the redline RPM. If this occurs an immediate sharp pull up should be initiated in order to reduce airspeed and thus RPM. Prop RPM will now be controlled by airspeed as well as throttle position.
Since light aircraft use engine oil pressure to control the prop a hunting prop (ie uncommanded RPM excursions above and/or below the selected RPM) can be a sign of dropping oil pressure and therefore the engine oil pressure should be immediately checked if the prop is not operating normally.
It is also important to know which prop type, Mcaulley, or Hartzell is on your aircraft as they work in opposite ways. A decrease in oil pressure will cause a
Mcaulley prop to go to course or low pitch. The Hatzell will go to fine pitch or high RPM with the loss of oil pressure.
In Multi engine aircraft an overspeeding prop should be feathered immediately (except for an overspeed right after takeoff) .