Move to employ one Australian flier (6)
I believe the answer is:
budgie
'australian flier' is the definition.
(Australian bird)
'move to employ one' is the wordplay.
'move' becomes 'budge' (budging is a kind of moving).
'to employ' is an insertion indicator.
'one' becomes 'I' (Roman numeral).
'budge' placed around 'i' is 'BUDGIE'.
(Other definitions for budgie that I've seen before include "Popular cage-bird from Australia" , "Small bird, domestic favourite" , "Common Australian cage-bird" , "Small domestic parakeet" , "Pet cage-bird from Australia" .)