Change bill by a whisker (6)
I believe the answer is:
adjust
'change' is the definition.
(adjusting is a kind of changing)
'bill by a whisker' is the wordplay.
'bill' becomes 'ad' (advertisement stuck on wall).
'by a whisker' becomes 'just' (I've seen this before).
'ad'+'just'='ADJUST'
(Other definitions for adjust that I've seen before include "Change slightly to fit" , "Alter by small amount to make right for use" , "Bring small change" , "Make small changes" , "Regulate, alter by small amount" .)