Voice of Cornish banker having argument (8)
I believe the answer is:
falsetto
'voice' is the definition.
(falsetto is a kind of voice)
'cornish banker having argument' is the wordplay.
'cornish banker' becomes 'Fal' (River Fal in Cornwall, something which 'banks').
'having' says to put letters next to each other.
'argument' becomes 'setto' (set-to can mean a fight or argument).
'fal'+'setto'='FALSETTO'
'of' is the link.
(Other definitions for falsetto that I've seen before include "Artificially high voice of latest sort" , "Voice that's raised" , "High vocal range" , "Unnatural voice" , "high notes?" .)