Argument has girl coming out worried (6)
I believe the answer is:
debate
'argument' is the definition.
(synonyms)
'girl coming out worried' is the wordplay.
'girl coming out' becomes 'deb' (short for debutante).
'worried' becomes 'ate' (something worrying may eat someone up).
'deb'+'ate'='DEBATE'
'has' acts as a link.
(Other definitions for debate that I've seen before include "Public discussion, perhaps a contest" , "Discuss through argument" , "Hold public discussion about" , "A public discussion about a topic" , "Discuss (in parliament)" .)