Dicky loved Italian city's cycling stadium (9)
I believe the answer is:
velodrome
'cycling stadium' is the definition.
(a velodrome is a stadium for cycling)
'dicky loved italian city's' is the wordplay.
'dicky' is an anagram indicator (dicky can mean ill or non-functioning).
'italian city' becomes 'rome' (city in Italy).
'loved' with letters rearranged gives 'velod'.
'velod'+'rome'='VELODROME'
(Other definitions for velodrome that I've seen before include "Stadium containing a cycle-racing track" , "Cycle stadium" , "Banked oval track for cycle racing" , "Cycling arena" .)