Dispute rumour accepted by people with wealth (4,5)
I believe the answer is:
have words
'dispute' is the definition.
(thesaurus)
'rumour accepted by people with wealth' is the wordplay.
'rumour' becomes 'word' (the word on the street).
'accepted by' indicates putting letters inside (inserted letters are accepted).
'people with wealth' becomes 'haves' (as opposed to the have-nots).
'word' going inside 'haves' is 'HAVE WORDS'.
(Other definitions for have words that I've seen before include "What lexicographers need to" , "Quarrel, engage in verbal altercation" .)