Monkey: one pursuing bird (4)
I believe the answer is:
titi
'monkey' is the definition.
(I know that titi is a type of New World monkey)
'one pursuing bird' is the wordplay.
'one' becomes 'i' (Roman numeral).
'pursuing' says to put letters next to each other.
'bird' becomes 'tit' (tit is a kind of bird).
'i' put after 'tit' is 'TITI'.
(Other definitions for titi that I've seen before include "tree" , "Monkey" .)