An animal and one dicky bird! (6)
I believe the answer is:
pigeon
'bird' is the definition.
(pigeon is a kind of bird)
'an animal and one dicky' is the wordplay.
'an animal' becomes 'pig' (I've seen this in other clues**).
'and' means one lot of letters go next to another.
'dicky' is an anagram indicator (dicky can mean ill or non-functioning).
'one' anagrammed gives 'eon'.
'pig'+'eon'='PIGEON'
(Other definitions for pigeon that I've seen before include "Short-legged bird" , "Baby" , "Seed-eating bird" , "Common dove" , "See 1 Across" .)