Avoid first woman to have a key (5)
I believe the answer is:
evade
'avoid' is the definition.
(I know that avoid is the is a more specific form of the action of evade.)
'woman to have a key' is the wordplay.
'woman' becomes 'Eve' (Eve is an example).
'to have' means one lot of letters goes inside another.
'key' becomes 'd' (musical key).
'a'+'d'='ad'
'eve' placed around 'ad' is 'EVADE'.
'first' acts as a link.
(Other definitions for evade that I've seen before include "Dodge by cleverness (5)" , "Avoid, get out of" , "Escape (something)" , "Fail to pay" , "Shun, escape" .)