Seen to have rushed round the capital of Italy (5)
I believe the answer is:
spied
'seen' is the definition.
(I've seen this before)
'rushed round the capital of italy' is the wordplay.
'rushed' becomes 'sped' ('speed' can be a synonym of 'rush'**).
'round' is an insertion indicator.
'the capital of' indicates taking the first letters.
The initial letter of 'italy' is 'i'.
'sped' going around 'i' is 'SPIED'.
'to have' is the link.
(Other definitions for spied that I've seen before include "Watched secretly" , "Noticed" , "Seen" , "Caught sight of" , "Was a secret agent" .)