Bear out one’s gone in to cook (6)
I believe the answer is:
braise
'cook' is the definition.
(braising is a kind of cooking)
'bear out one's gone in' is the wordplay.
'out' indicates an anagram (out can mean wrong or inaccurate).
'one's' becomes 'is' (roman numeral).
'gone in' indicates putting letters inside.
'bear' anagrammed gives 'brae'.
'brae' placed around 'is' is 'BRAISE'.
'to' is the link.
(Other definitions for braise that I've seen before include "Stew in a closed pan" , "Rabies (anag.)" , "Heat slowly" , "Fry then stew slowly" , "Fry and then stew (food)" .)