Know-how that hurts in the media (7)
I believe the answer is:
prowess
'know-how' is the definition.
(thesaurus)
'that hurts in the media' is the wordplay.
'that hurts' becomes 'ow'.
'in the' means one lot of letters goes inside another.
'media' becomes 'press' (I've seen this before).
'ow' inserted within 'press' is 'PROWESS'.
(Other definitions for prowess that I've seen before include "Acquired skill(s)" , "Ability, expertise" , "Mastery - talent" , "Accomplishment" , "Great ability or daring" .)