Snake swallowing head of animal quickly (4)
I believe the answer is:
asap
'quickly' is the definition.
(as soon as possible)
'snake swallowing head of animal' is the wordplay.
'snake' becomes 'asp' (asp is a kind of snake).
'swallowing' means one lot of letters goes inside another.
'head of' indicates taking the first letters.
The initial letter of 'animal' is 'a'.
'asp' enclosing 'a' is 'ASAP'.
(Other definitions for asap that I've seen before include "Notation meaning with minimum delay" , "yesterday?" , "As soon as possible (abbrev.)" , "'As quickly as you can, initially (4)'" , "Notation for urgent, quick as you can (4)" .)