International hotel supports my city (7)
I believe the answer is:
corinth
'city' is the definition.
(Corinth is an example)
'international hotel supports my' is the wordplay.
'international' becomes 'int' (abbreviation for international).
'hotel' becomes 'h' (phonetic alphabet: alpha, bravo, charlie etc.).
'supports' is a charade indicator (letters next to each other) (bottom letters provide a support for the top ones).
'my' becomes 'cor' (both are expressions of surprise).
'int'+'h'='inth'
'inth' after 'cor' is 'CORINTH'.
(Other definitions for corinth that I've seen before include "City of Greece" , "Greek port and city, important since classical times" , "Ancient Greek city" , "Region of ancient Greece" , "Greek Gulf, isthmus city" .)