One with inclination to drop a bird (4)
I believe the answer is:
ibis
'bird' is the definition.
(ibis is a kind of bird)
'one with inclination to drop a' is the wordplay.
'one with' becomes 'i' (I've seen this in other clues**).
'inclination' becomes 'bias' (bias is a kind of inclination).
'to drop' suggests deleting specific letters.
'bias' with 'a' taken away is 'bis'.
'i'+'bis'='IBIS'
(Other definitions for ibis that I've seen before include "Sacred Egyptian bird" , "Storklike bird" , "Slowly discharge" , "Bird worshipped in Ancient Egypt" , "Flier" .)