Argued about a red nose (8)
I believe the answer is:
reasoned
'argued' is the definition.
('reason' can be a synonym of 'argue')
'about a red nose' is the wordplay.
'about' is an anagram indicator.
'a'+'red'+'nose'='arednose'
'arednose' is an anagram of 'REASONED'.
(Other definitions for reasoned that I've seen before include "Dear ones (anag)" , "Based on logic" , "Logically valid" , "Explained logically" , "clear" .)