Ramble around Rome, say (4)
I believe the answer is:
roam
'ramble' is the definition.
(I know that ramble can be written as roam)
'rome say' is the wordplay.
'say' shows a homophone (sound like).
'rome' is a homophone of 'ROAM'.
'around' acts as a link.
(Other definitions for roam that I've seen before include "Walk without a specific destination" , "Travel widely" , "Move about aimlessly" , "Stray" , "go on walkabout" .)