Apparent movement of a free gyroscope
Once gains spinning, North end of spin axis of a free gyroscope will remain pointing towards fixed direction in space due to gyroscopic inertia. (Star)
As long as no force/torque is applied.
Due to earth rotation, To an observer on the earth, the star appear to move.
During 24 hour period, the Altitude and Azimuth of star will change.
The star will trace out a circular path.
So, North end of spin axis of a free gyroscope will also trace out a circular path.
Depending on the observer latitude and star declination, the trace out circular path will be above horizon or below horizon.