Exposed relative's endless bill (6)
I believe the answer is:
unclad
'exposed' is the definition.
(unclothing is a kind of exposing)
'relative's endless bill' is the wordplay.
'relative' becomes 'uncle' (uncle is a kind of relative).
'endless' means to remove the last letter.
'bill' becomes 'ad' (advertisement stuck on wall).
'uncle' with its last letter taken off is 'uncl'.
'uncl'+'ad'='UNCLAD'
(Other definitions for unclad that I've seen before include "Not wearing clothes" , "Uncovered" , "with nothing on" , "nude" , "having abandoned habit" .)