Very old ruined city containing Etruria's first arena (9)
I believe the answer is:
velodrome
'arena' is the definition.
(I've seen this before)
'very old ruined city containing etruria's first' is the wordplay.
'very' becomes 'v' (common abbreviation).
'ruined' is an anagram indicator.
'city' becomes 'rome' (Rome is an example).
'containing' is an insertion indicator.
'first' suggests taking the first letters.
The first letter of 'etruria' is 'e'.
'old' with letters rearranged gives '[old]'.
'[old]'+'rome'='lodrome'
'lodrome' going around 'e' is 'elodrome'.
'v'+'elodrome'='VELODROME'
(Other definitions for velodrome that I've seen before include "Stadium containing a cycle-racing track" , "Cycling arena" , "Banked oval track for cycle racing" , "Cycle stadium" .)