Leftover making men rant wildly (7)
I believe the answer is:
remnant
'leftover' is the definition.
(synonyms)
'men rant wildly' is the wordplay.
'wildly' is an anagram indicator.
'men'+'rant'='menrant'
'menrant' with letters rearranged gives 'REMNANT'.
'making' is the link.
(Other definitions for remnant that I've seen before include "Piece of cloth left over" , "Leftovers" , "Piece or people left over" , "faithful minority" , "Men rant poorly when it's left over" .)