Southern queen with capacity to grasp bishop’s argument (8)
I believe the answer is:
squabble
'argument' is the definition.
(thesaurus)
'southern queen with capacity to grasp bishop's' is the wordplay.
'southern' becomes 's' (abbreviation).
'queen' becomes 'qu' (abbreviation for queen).
'with capacity' becomes 'able'.
'to grasp' is an insertion indicator.
'bishop' becomes 'b' (abbreviation used in chess).
'able' placed around 'b' is 'abble'.
's'+'qu'+'abble'='SQUABBLE'
(Other definitions for squabble that I've seen before include "Bicker" , "Quarrel in petty or noisy way" , "Quarrel about petty points" , "Have a minor row" , "Argue over petty things" .)