Parker cooked hot fish outside (7)
I believe the answer is:
dorothy
'parker' is the definition.
(Dorothy Parker)
'cooked hot fish outside' is the wordplay.
'cooked' is an anagram indicator.
'fish' becomes 'dory' (dory is a kind of fish**).
'outside' indicates putting letters inside.
'hot' with letters rearranged gives 'oth'.
'oth' put into 'dory' is 'DOROTHY'.
(Other definitions for dorothy that I've seen before include "Wizard of Oz child" , "Girl from Kansas" , "one of 5d's troupe" , "Woman" , "Name of the young heroine in 'The Wizard of Oz'" .)