Carry out an order for early closing (4)
I believe the answer is:
obey
'carry out' is the definition.
(I've seen this before)
'an order for early closing' is the wordplay.
'an order' becomes 'obe' (Order of the British Empire award).
'for' says to put letters next to each other.
'closing' indicates one should take the final letters (the letter which ends or closes the word).
The final letter of 'early' is 'y'.
'obe'+'y'='OBEY'
(Other definitions for obey that I've seen before include "Perversely inclined to do the opposite" , "Do as one's told" , "Conform" , "Submit to authority" , "Heed" .)