Almost hungry, having bagged large bird (5)
I believe the answer is:
eagle
'bird' is the definition.
(eagle is a kind of bird)
'almost hungry having bagged large' is the wordplay.
'almost' means to remove the last letter (most of the word but not all of it).
'hungry' becomes 'eager' (I've seen this before).
'having bagged' indicates putting letters inside.
'large' becomes 'l'.
'eager' with its last letter taken off is 'eage'.
'eage' enclosing 'l' is 'EAGLE'.
(Other definitions for eagle that I've seen before include "Score of two strokes under par for a golf hole" , "Erne, perhaps" , "High-flyer" , "Bald, golden, bird" , "Aglee (anag.)" .)