Bird annoyed by account (9)
I believe the answer is:
crossbill
'bird' is the definition.
(crossbill is a kind of bird)
'annoyed by account' is the wordplay.
'annoyed' becomes 'cross' (I've seen this before).
'by' says to put letters next to each other.
'account' becomes 'bill' (billing is a kind of accounting**).
'cross'+'bill'='CROSSBILL'
(Other definitions for crossbill that I've seen before include "Flier" , "Type of finch" , "bird" , "Flyer" .)