Dodge first woman with a key (5)
I believe the answer is:
evade
'dodge' is the definition.
('evade' can be a synonym of 'dodge')
'first woman with a key' is the wordplay.
'first woman' becomes 'eve' (I've seen this before**).
'with' is an insertion indicator.
'key' becomes 'd' (I've seen this in other clues).
'a'+'d'='ad'
'eve' going around 'ad' is 'EVADE'.
(Other definitions for evade that I've seen before include "Escape, avoid" , "Shirk" , "Dodge, stay clear of" , "Avoid, get out of" , "To get away from" .)