One with a big head, bird swallowed grandpa! (8)
I believe the answer is:
popinjay
'one with a big head bird swallowed grandpa' is the definition.
I can't judge whether this defines the answer.
'one with a big head bird' is the wordplay.
'one with' is a charade indicator (letters next to each other).
'a big head' becomes 'popin' (I am not sure about this - if you are sure you should give a lot more credence to this answer).
'bird' becomes 'jay' (jay is a kind of bird).
'popin' next to 'jay' is 'POPINJAY'.
Can you help me to learn more?
(Other definitions for popinjay that I've seen before include "vain sort" , "Coxcomb" , "One super-smart" , "Strutting fop" , "Conceited person" .)