Nibbled, accepting a lure (4)
I believe the answer is:
bait
'lure' is the definition.
('bait' can be a synonym of 'lure')
'nibbled accepting a' is the wordplay.
'nibbled' becomes 'bit' (I've seen this in other clues).
'accepting' indicates putting letters inside.
'bit' enclosing 'a' is 'BAIT'.
(Other definitions for bait that I've seen before include "Used to lure fish or other animals into danger" , "Worms, for example" , "Boilie, for example" , "Food used as lure" , "Lure; deliberately taunt" .)