Twice cook very old bird (4)
I believe the answer is:
dodo
'very old bird' is the definition.
'twice cook' is the wordplay.
'twice' says to double the letters.
'cook' becomes 'do' (I've seen this in other clues).
'do' duplicated is 'DODO'.
(Other definitions for dodo that I've seen before include "Square" , "Repetitive extinct animal" , "Ultra-conservative" , "E [EXTINCT] bird" , "silly person" .)