Exhausted genteel American behind mirror (5)
I believe the answer is:
glass
'mirror' is the definition.
(looking glass)
'exhausted genteel american behind' is the wordplay.
'exhausted' says to hollow out the word (remove centre letters) (the word is emptied out or exhausted).
'american behind' becomes 'ass' (primarily US term for one's behind).
'genteel' with its centre removed is 'gl'.
'gl'+'ass'='GLASS'
(Other definitions for glass that I've seen before include "Philip --, US composer" , "Balloon, say" , "Brittle transparent material" , "Transparent substance" , "barometer" .)