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' means one lot of letters goes inside another.
'the capital of italy' becomes 'i' (I am not sure about this - if you are sure you should give a lot more credence to this answer).
'sped' going around 'i' is 'SPIED'.
'to have' is the link.
Can you help me to learn more?
(Other definitions for spied that I've seen before include "Watched secretly" , "Noticed" , "Seen" , "Caught sight of" , "Was a secret agent" .)