On the radio, shopkeeper is more boorish (7)
I believe the answer is:
grosser
'more boorish' is the definition.
Both the answer and definition are comparative adjectives. Perhaps you can see an association between them that I don't see?
'on the radio shopkeeper' is the wordplay.
'on the radio' shows a homophone (sound like).
'shopkeeper' becomes 'grocer' (I've seen this before).
'grocer' is a homophone of 'GROSSER'.
'is' is the link.
Can you help me to learn more?
(Other definitions for grosser that I've seen before include "more vulgar" , "More corpulent" .)