Is there a free shuttle we can take from HKIA to Yau Ma Tei? Any guidance is greatly appreciated

There is no free shuttle bus from HKIA to Yau Ma Tei.
You are suggested to take shuttle bus no.A21 at Airport (Ground Transportation Centre), get off at Man Ming Lane, Nathan Road. The trip takes around 55 mins. It costs 33 HKD per person. After arriving, walk north along Nathan Road around 100 yards (90 meters) to find the destination.