In the shortest time (4)

I believe the answer is:

asap

(Other definitions for asap that I've seen before include "Initials notation meaning with all possible speed" , "Common acronym for quick-as-you-can" , "Notation for as quickly as you can" , "'As quickly as you can, initially (4)'" , "Notation for urgent, quick as you can (4)" .)

I've seen this clue in The Mirror.

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