Demolish half of Rhodes, ancient city (7)
I believe the answer is:
destroy
'demolish' is the definition.
(I know that demolish can be written as destroy)
'half of rhodes ancient city' is the wordplay.
'half of' suggests halving the letters.
'ancient city' becomes 'Troy' (Troy was an ancient city).
'rhodes' with half the letters taken is 'des'.
'des'+'troy'='DESTROY'
(Other definitions for destroy that I've seen before include "Get rid of" , "Flatten" , "Soundly defeat" , "Kill; ruin" , "Demolish; pull down" .)