Area of corporation hearing of extravagance (5)
I believe the answer is:
waist
'area of corporation' is the definition.
(corporation can informally mean body fat)
'hearing of extravagance' is the wordplay.
'hearing of' shows a homophone (sound like).
'extravagance' becomes 'waste' (extravagance can mean waste or excess).
'waste' is a homophone of 'WAIST'.
(Other definitions for waist that I've seen before include "Middle part of a ship" , "Between ribs and hips" , "Band may go round here" , "Spare tyre location?" , "Ever-expanding middle" .)