Bitter found to have no head (4)
I believe the answer is:
tart
'bitter' is the definition.
(tart can mean bitter-tasting)
'found to have no head' is the wordplay.
'found' becomes 'start' (as in to establish).
'to have no head' means to remove the first letter (I've seen 'has no head' mean this).
'start' with its initial letter taken off is 'TART'.
(Other definitions for tart that I've seen before include "Sharp or sour in taste" , "Pie with fruit filling" , "Sort of girl" , "Flat pie" , "Acidic; pastry dish" .)