Parrot's bill stuck in mouth (5)
I believe the answer is:
macaw
'parrot's' is the definition.
(macaw is a kind of parrot)
'bill stuck in mouth' is the wordplay.
'bill' becomes 'ac'.
'stuck in' means one lot of letters goes inside another.
'mouth' becomes 'maw' (maw is a kind of mouth).
'ac' going into 'maw' is 'MACAW'.
(Other definitions for macaw that I've seen before include "Large colourful parrot" , "Type of parrot" , "Brightly-coloured parrot" , "Long-tailed American parrot" , "brilliant winger" .)