Bite of Conservative cut (4)
I believe the answer is:
chew
'bite' is the definition.
(I know that chew is a type of bite)
'conservative cut' is the wordplay.
'conservative' becomes 'C' (UK political abbreviation).
'cut' becomes 'hew' (hew can mean to chop or cut).
'c'+'hew'='CHEW'
'of' is the link.
(Other definitions for chew that I've seen before include "Treat for dog" , "Process food" , "Bite and grind food in the mouth" , "Bite repeatedly" , "Ruminate" .)