Piercing cry that hurt head of little bird (7,3)
I believe the answer is:
screech owl
'bird' is the definition.
(screech owl is a type of owl)
'piercing cry that hurt head of little' is the wordplay.
'piercing cry' becomes 'screech' (a screech is loud or shrill cry).
'that hurt' becomes 'ow' (exclamation of pain).
'head of' indicates taking the first letters.
The initial letter of 'little' is 'l'.
'screech'+'ow'+'l'='SCREECH-OWL'
(Other definitions for screech owl that I've seen before include "Eg, Tyto alba; howls recce (anag.)" , "Bird of prey" .)