Youngster to yearn endlessly for ruined city (7)
I believe the answer is:
babylon
'ruined city' is the definition.
(ancient city)
'youngster to yearn endlessly' is the wordplay.
'youngster' becomes 'baby'.
'to yearn' becomes 'long' (synonyms).
'endlessly' means to remove the last letter.
'long' with its final letter removed is 'lon'.
'baby'+'lon'='BABYLON'
'for' is the link.
(Other definitions for babylon that I've seen before include "Bony lab found in the ancient city" , "Ancient city in what is now Iraq noted for wealth and wickedness" , "Site of hanging gardens" , "Ancient Mesopotamian city" , "Ancient city on Euphrates once noted for sin and wickedness" .)