Argued with old socialite who's taken on an old rocker (7)
I believe the answer is:
debated
'argued' is the definition.
('debate' can be a synonym of 'argue')
'old socialite who's taken on an old rocker' is the wordplay.
'old socialite who' becomes 'deb' (I am not sure about this - if you are sure you should give a lot more credence to this answer).
'taken on' is a charade indicator (letters next to each other).
'an' becomes 'a'.
'old rocker' becomes 'ted' (member of the Teddy boy subculture).
'deb'+'a'+'ted'='DEBATED'
'with' is the link.
Can you help me to learn more?
(Other definitions for debated that I've seen before include "Discussed in public" , "Considered" , "Discussed formally" , "Argued" , "Contemplated" .)