Snake bites one without delay (4)
I believe the answer is:
asap
'without delay' is the definition.
(as soon as possible)
'snake bites one' is the wordplay.
'snake' becomes 'asp' (asp is a kind of snake).
'bites' indicates putting letters inside.
'one' becomes 'a' (a thing is one thing).
'asp' enclosing 'a' is 'ASAP'.
(Other definitions for asap that I've seen before include "At one's earliest convenience" , "Notation meaning without delay, fast as you can" , "At the earliest opportunity (abbrev.)" , "Notation for urgent, quick as you can (4)" , "Notation-acronym meaning without delay" .)