Moving to Milan, one gutted to move (9)
I believe the answer is:
emotional
'moving' is the definition.
('emotional' is associated in meaning with 'moving')
'milan one gutted to move' is the wordplay.
'gutted' means to remove the middle letters (to gut something is to remove its insides).
'move' indicates an anagram.
'one' with its centre removed is 'oe'.
'milan'+'oe'+'to'='milanoeto'
'milanoeto' with letters rearranged gives 'EMOTIONAL'.
'to' is the link.
(Other definitions for emotional that I've seen before include "Dramatic" , "Showing feelings like love or fear" , "tear-jerking" , "Subject to intense feelings" , "Loving" .)