Has moved parrot on in hurry (5,1,3)
I believe the answer is:
shake a leg
'hurry' is the definition.
(I've seen this in another clue)
'has moved parrot on' is the wordplay.
'moved' is an anagram indicator.
'parrot' becomes 'kea' (kea is a kind of parrot).
'on' becomes 'leg' (cricket term, fielding positions).
'has' with letters rearranged gives 'sha'.
'sha'+'kea'+'leg'='SHAKE A LEG'
'in' is the link.
(Other definitions for shake a leg that I've seen before include "Get a move on" , "Hurry up" , "Get up - be productive" .)