Travel around capital, reportedly (4)
I believe the answer is:
roam
'travel around' is the definition.
(I've seen this in another clue)
'capital reportedly' is the wordplay.
'capital' becomes 'Rome' (capital of Italy).
'reportedly' shows a homophone (sound like).
'rome' sounds like 'ROAM'.
(Other definitions for roam that I've seen before include "Wander freely" , "'Wander, ramble (4)'" , "Prowl" , "Wander widely" , "Meander" .)