As it happens, desperately poor left city (9)
I believe the answer is:
liverpool
'city' is the definition.
(Liverpool is an example)
'as it happens desperately poor left' is the wordplay.
'as it happens' becomes 'live' (as in live broadcasting).
'desperately' is an anagram indicator.
'left' becomes 'l' (common abbreviation).
'poor' is an anagram of 'rpoo'.
'live'+'rpoo'+'l'='LIVERPOOL'
(Other definitions for liverpool that I've seen before include "team" , "Merseyside port" , "city with two cathedrals" , "Merseyside city of The Beatles" , "Side" .)