Cooking, Delia suffered (5)
I believe the answer is:
ailed
'suffered' is the definition.
(ailing is a kind of suffering)
'cooking delia' is the wordplay.
'cooking' indicates anagramming the letters (letters cooked up into a new form).
'delia' anagrammed gives 'AILED'.
(Other definitions for ailed that I've seen before include "Felt bad" , "Was ill" , "Became sick" , "was giving trouble" , "was on the blink?" .)