Sink getting old food (4)
I believe the answer is:
sago
'food' is the definition.
(I've seen this before)
'sink getting old' is the wordplay.
'sink' becomes 'sag' (sagging is a kind of sinking).
'getting' is a charade indicator (letters next to each other).
'old' becomes 'o' (common abbreviation eg in OE for Old English).
'sag'+'o'='SAGO'
(Other definitions for sago that I've seen before include "Starchy grain used in desserts" , "Starchy cereal used in puddings" , "Starchy foodstuff" , "Palm cereal" , "Type of milk pudding" .)