Argument over object in West Sussex (8)
I believe the answer is:
worthing
'in west sussex' is the definition.
(West Sussex town)
'argument over object' is the wordplay.
'argument' becomes 'row' (I've seen this before).
'over' says the letters should be written in reverse.
'object' becomes 'thing'.
'row' written backwards gives 'wor'.
'wor'+'thing'='WORTHING'
(Other definitions for worthing that I've seen before include "Seaside resort in West Sussex" , "one mislaid at Victoria" .)