For example, Sebastian Drive, backing onto ancient city (not eastern) (6)
I believe the answer is:
martyr
'for example sebastian' is the definition.
(St Sebastian is an example)
'drive backing onto ancient city not eastern' is the wordplay.
'drive backing' becomes 'mar' (I can't justify this - if you can you should believe this answer much more).
'onto' is a charade indicator (letters next to each other).
'ancient city' becomes 'tyre' (ancient city in modern-day Lebanon).
'not' suggests deleting specific letters.
'eastern' becomes 'e'.
'tyre' with 'e' removed is 'tyr'.
'mar'+'tyr'='MARTYR'
(Other definitions for martyr that I've seen before include "Sufferer for faith" , "Victim for a cause" , "Victim; eg St Stephen" , "put at stake?" , "Person who dies for a cause" .)