Took advantage of American cheese, removing half (4)
I believe the answer is:
used
'took advantage of' is the definition.
(I've seen this in another clue)
'american cheese removing half' is the wordplay.
'american' becomes 'us' (abbreviation for United States).
'cheese' becomes 'edam' (Edam is an example).
'removing half' suggests halving the letters.
'edam' with half the letters taken is 'ed'.
'us'+'ed'='USED'
(Other definitions for used that I've seen before include "Dues (anag.)" , "Old" , "Scottish expert" , "Utilised" , "Enjoyed" .)