Singer in argument after footballers left (8)
I believe the answer is:
falsetto
'singer' is the definition.
(someone who sings with a false high voice)
'argument after footballers left' is the wordplay.
'argument' becomes 'set to' (I've seen this before).
'after' means one lot of letters go next to another.
'footballers' becomes 'FA' (Football Association abbreviation).
'left' becomes 'L' (common abbreviation).
'fa'+'l'='fal'
'setto' put after 'fal' is 'FALSETTO'.
'in' is the link.
(Other definitions for falsetto that I've seen before include "Abnormally high voice" , "Strained sentiment" , "Voice pitch higher than the normal range" , "Forcedly high voice" , "high notes?" .)