Argument inspector advanced in Home Counties (7)
I believe the answer is:
dispute
'argument' is the definition.
(I've seen this before)
'inspector advanced in home counties' is the wordplay.
'inspector' becomes 'di' (I've seen this in other clues).
'advanced' becomes 'put' (as in to put forward or advance an idea).
'in' is an insertion indicator.
'home counties' becomes 'se' (Home Counties in the South East of England).
'put' put into 'se' is 'spute'.
'di'+'spute'='DISPUTE'
(Other definitions for dispute that I've seen before include "Question or deny accuracy or validity" , "Altercate" , "conflict" , "Quarrel over rights" , "Disagree or challenge" .)