Dog bites messenger dropping off her flier (4,5)
I believe the answer is:
bald eagle
'flier' is the definition.
(bald eagle is a kind of birdanimal)
'dog bites messenger dropping off her' is the wordplay.
'dog' becomes 'beagle' (beagle is a kind of dog**).
'bites' means one lot of letters goes inside another.
'messenger' becomes 'herald' (herald is a kind of messenger).
'dropping off' indicates named letters should be taken away.
'herald' with 'her' taken out is 'ald'.
'beagle' going around 'ald' is 'BALD EAGLE'.
(Other definitions for bald eagle that I've seen before include "National emblem of the USA" , "N. American bird" , "Flier" , "US national bird" , "National bird of the USA" .)