A song from men circulating with hat (6)
I believe the answer is:
anthem
'a song' is the definition.
(anthem is a kind of song)
'men circulating with hat' is the wordplay.
'circulating with' indicates an anagram.
'men' with its letters mixed up with 'hat' gives 'ANTHEM'.
'from' is the link.
(Other definitions for anthem that I've seen before include "Song of praise or loyalty" , "Choral work" , "Hymn of loyalty" , "One for doomed youth" , "National melody" .)