Much obliged to a hunky criminal (5,3)
I believe the answer is:
'much obliged' is the definition.
(I've seen this before)
'to a hunky criminal' is the wordplay.
'criminal' indicates anagramming the letters.
'toahunky' with letters rearranged gives 'THANK-YOU'.
(Other definitions for thank you that I've seen before include "Much obliged!" , "Polite reply (to gift)" , "Words of acknowledgement" , "Concentional expression of appreciation" , "Ta" .)