Carry out an order to the very end (4)
I believe the answer is:
obey
'carry out' is the definition.
(I've seen this in another clue)
'an order to the very end' is the wordplay.
'an order' becomes 'obe' (Order of the British Empire award).
'to' is a charade indicator (letters next to each other).
'end' says to take the final letters.
The last letter of 'very' is 'y'.
'obe'+'y'='OBEY'
(Other definitions for obey that I've seen before include "Do as you're told!" , "Follow orders" , "Act in accordance with (law)" , "Do as ordered" , "Submit to authority" .)