Avoid lady accepting notice (5)
I believe the answer is:
evade
'avoid' is the definition.
(evading is a kind of avoiding)
'lady accepting notice' is the wordplay.
'lady' becomes 'eve' (I've seen this before**).
'accepting' means one lot of letters goes inside another.
'notice' becomes 'ad'.
'eve' placed around 'ad' is 'EVADE'.
(Other definitions for evade that I've seen before include "Sidestep" , "Dodge by cleverness (5)" , "Shun, escape" , "Fail to pay" , "Dodge, steer clear of" .)