One of the family cooked tuna (4)
I believe the answer is:
aunt
'one of the family' is the definition.
'cooked tuna' is the wordplay.
'cooked' indicates an anagram (letters cooked into a new form).
'tuna' anagrammed gives 'AUNT'.
(Other definitions for aunt that I've seen before include "Tuna for the odd relative" , "Close relative" , "Wife of one's uncle" , "Blood relative" , "Sister of father/mother" .)