Kept feeding pig, constant companion (6)
I believe the answer is:
shadow
'constant companion' is the definition.
'kept feeding pig' is the wordplay.
'kept' becomes 'had' (I've seen this before).
'feeding' means one lot of letters goes inside another (one word is fed by another set of letters).
'pig' becomes 'sow' (I've seen this in another clue).
'had' inserted inside 'sow' is 'SHADOW'.
(Other definitions for shadow that I've seen before include "Opposer" , "It's cast when light is blocked" , "Hint, remnant; follow secretly" , "Ghost" , "Dark area - follow secretly" .)