Shellfish, ordinarily gutted, with rest cooked (6)
I believe the answer is:
oyster
'shellfish' is the definition.
(oyster is a kind of shellfish)
'ordinarily gutted with rest cooked' is the wordplay.
'gutted' means to remove the middle letters (to gut something is to remove its insides).
'with' means one lot of letters go next to another.
'cooked' is an anagram indicator (letters cooked into a new form).
'ordinarily' with its centre removed is 'oy'.
'rest' anagrammed gives 'ster'.
'oy'+'ster'='OYSTER'
(Other definitions for oyster that I've seen before include "Pearl-yielding shellfish" , "person unwilling to communicate" , "Pearl-producing bivalve" , "Capital card" , "Seafood item sometimes eaten alive" .)