Raffish rogue, cool entering car, shows breeding (4,7)

'breeding' is the definition.
(breeding fish)

'raffish rogue cool entering car' is the wordplay.
'rogue' indicates an anagram (letters go rogue).
'cool' becomes 'in' ('in' can mean fashionable or cool).
'entering' is an insertion indicator.
'car' becomes 'mg'.
'in' put within 'mg' is 'ming'.
'raffish' with letters rearranged gives 'fishfar'.
'fishfar'+'ming'='FISH-FARMING'

'shows' is the link.