Regularly reimburse Australian natives (4)
I believe the answer is:
emus
'australian natives' is the definition.
(native australian bird)
'regularly reimburse' is the wordplay.
'regularly' means one should take alternating letters (regularly take one letter, leave next etc.).
The alternate letters of 'reimburse' are 'EMUS'.
(Other definitions for emus that I've seen before include "Muse about flightless Australian birds" , "Running birds" , "laboratory units" , "Largest native Australian birds" , "Aussie birds" .)