Chief ingredient of Cheddar cheese (4)
I believe the answer is:
arch
'chief' is the definition.
('arch' can be a synonym of 'chief')
'ingredient of cheddar cheese' is the wordplay.
'ingredient of' indicates the answer is hidden within the clue.
'ARCH' can be found hidden inside 'cheddar cheese'.
(Other definitions for arch that I've seen before include "Marble, for example" , "Curved masonry construction" , "Shrewd; bridge" , "Curve spanning an opening" , "Prefix meaning chief - maybe an angel" .)