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 (cook can mean to falsify or distort).
'delia' with letters rearranged 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?" .)