First Lady inspiring Bill’s escape (5)
I believe the answer is:
evade
'escape' is the definition.
(I know that evade is a more specific form of escape)
'first lady inspiring bill's' is the wordplay.
'first lady' becomes 'eve' (Biblical first woman).
'inspiring' is an insertion indicator.
'bill' becomes 'ad' (advertisement stuck on wall).
'eve' going around 'ad' is 'EVADE'.
(Other definitions for evade that I've seen before include "Manage to avoid" , "Escape (esp. by guile)" , "Dodge - prevaricate" , "Dodge or equivocate" , "Get round" .)