To argue madly, leading to assault (7)
I believe the answer is:
outrage
'assault' is the definition.
(outraging is a kind of assaulting)
'to argue madly' is the wordplay.
'madly' indicates anagramming the letters.
'to'+'argue'='toargue'
'toargue' is an anagram of 'OUTRAGE'.
'leading to' is the link.
(Other definitions for outrage that I've seen before include "Act that shocks public opinion, generates anger" , "Deplorable insult" , "To argue about act that shocks public opinion" , "Gross injury" , "furious reaction" .)