Snake biting one without delay (4)
I believe the answer is:
asap
'without delay' is the definition.
(as soon as possible)
'snake biting one' is the wordplay.
I cannot quite see how this works, but
'one' could be 'a' (a thing is one thing) and 'a' is present in the answer.
The remaining letters 'sap' is a valid word which might be clued in a way I don't see.
This explanation may well be incorrect...
(Other definitions for asap that I've seen before include "Notation or acronym meaning without avoidable delay" , "At the earliest opportunity (abbrev.)" , "Initials notation meaning with all possible speed" , "Notation for urgent, quick as you can (4)" , "'As quickly as you can, initially (4)'" .)