The first lady to eat a dead duck! (5)
I believe the answer is:
evade
'duck' is the definition.
('evade' can be a synonym of 'duck')
'the first lady to eat a dead' is the wordplay.
'the first lady' becomes 'eve' (I've seen this before**).
'to eat' means one lot of letters goes inside another.
'dead' becomes 'd'.
'a'+'d'='ad'
'eve' enclosing 'ad' is 'EVADE'.
(Other definitions for evade that I've seen before include "To get away from" , "Circumvent, dodge" , "Escape, avoid" , "Dodge, elude" , "Fail to pay" .)