Take exception to headless gift (6)
I believe the answer is:
resent
'take exception to' is the definition.
(I've seen this before)
'headless gift' is the wordplay.
'headless' means to remove the first letter.
'gift' becomes 'present' (present is a kind of gift).
'present' with its initial letter removed is 'RESENT'.
(Other definitions for resent that I've seen before include "Consider as an injury or affront" , "Find objectionable" , "Be offended by" , "Feel indignation at" , "Feel bitterness at (something)" .)