EMIT thanks, so (understandably) "under control of the appropriate authority" but no requirement to be be within the airport boundary.
AERODROME OBSTACLE CHART - ICAO
From CAP 168:-
A clearway need not have bearing strength and may be land or water. It may extend outside the aerodrome boundary only if the aerodrome authority establishes such control that will ensure that the clearway will be kept free from obstacles or that the clearway plane will not be infringed.