Elude first woman holding bill (5)
I believe the answer is:
evade
'elude' is the definition.
('evade' can be a synonym of 'elude')
'first woman holding bill' is the wordplay.
'first woman' becomes 'eve' (I've seen this before**).
'holding' indicates putting letters inside.
'bill' becomes 'ad' (advertisement stuck on wall).
'eve' going around 'ad' is 'EVADE'.
(Other definitions for evade that I've seen before include "Dodge by cleverness or trickery" , "Dodge, stay clear of" , "skirt" , "Dodge by cleverness (5)" , "Circumvent, dodge" .)