Sets out to find a Hardy heroine (4)
I believe the answer is:
tess
'a hardy heroine' is the definition.
(in Tess of the d'Urbervilles, Thomas Hardy novel)
'sets out' is the wordplay.
'out' indicates anagramming the letters (out can mean wrong or inaccurate).
'sets' with letters rearranged gives 'TESS'.
'to find' is the link.
(Other definitions for tess that I've seen before include "Lady" , "Hardy's pure woman" , "20 heroine" , "'Justice' finally done on her (Hardy)" , "Ill-starred Hardy heroine" .)