The old man on street's gone by (4)
I believe the answer is:
past
'gone by' is the definition.
(thesaurus)
'the old man on street's' is the wordplay.
'the old man' becomes 'pa' ('pa' can be a synonym of 'old man'**).
'on street' becomes 'st' (I've seen this in other clues).
'pa'+'st'='PAST'
(Other definitions for past that I've seen before include "Ended" , "A person's earlier life history" , "historical times" , "Yesteryear" , "over and done with" .)