Act slowly and prevaricate; intially not what this demanded (4)
I believe the answer is:
asap
If this is the answer I cannot explain how the clue works.
Can you help me to learn more?
(Other definitions for asap that I've seen before include "Notation or acronym meaning without avoidable delay" , "As soon as you can, initially" , "At one's earliest convenience" , "Notation for as quickly as you can" , "Notation-acronym meaning without delay" .)