If the 'airport' is a designated parachuting site, or if the para drop is a registered display, then in the UK and Europe at least, the rule is 'No props or rotors turning whilst parachuting is in progress.', which means in the air and on the ground (other than the drop aircraft of course.
Aeronautical maps / charts are clearly marked to show parachute centers, with an approximate three mile diameter 'exclusion zone' circled over them, and any display sites other than these centers are stated in the NOTAM for the relevant day(s).
A request has to be submitted to the CAA and any relevant ATC center for UK displays, providing information showing the display team name and registered number, the aircraft type and registration, departure airfield, DZ location and map reference, time slot for the display, and the altitude requested, the latter subject to weather, wind and availability with consideration to the location and other traffic.