Act slowly and prevaricate; initially not what this demanded (4)
I believe the answer is:
asap
'not what this demanded' is the definition.
I know nothing about this answer so I cannot judge whether it can be defined by this definition.
'act slowly and prevaricate initially' is the wordplay.
'initially' suggests taking the first letters.
The first letters of 'act slowly and prevaricate' is 'ASAP'.
Can you help me to learn more?
(Other definitions for asap that I've seen before include "As soon as you can, initially" , "Initials notation meaning with all possible speed" , "Notation meaning without delay, fast as you can" , "Common acronym for quick-as-you-can" , "Notation-acronym meaning without delay" .)