Avoid first woman carrying poster (5)
I believe the answer is:
evade
'avoid' is the definition.
(evading is a kind of avoiding)
'first woman carrying poster' is the wordplay.
'first woman' becomes 'eve' (I've seen this before**).
'carrying' means one lot of letters goes inside another.
'poster' becomes 'ad'.
'eve' placed around 'ad' is 'EVADE'.
(Other definitions for evade that I've seen before include "Keep away from" , "Dodge, elude" , "Dodge, keep clear of" , "Dodge, stay clear of" , "Fail to pay" .)