Insects originally exterminated snakes (4)
I believe the answer is:
asps
'snakes' is the definition.
(asp is a kind of snake)
'insects originally exterminated' is the wordplay.
'insects' becomes 'wasps' (wasp is a kind of insect).
'originally exterminated' means to remove the first letter (the original or first letter is removed).
'wasps' with its initial letter taken off is 'ASPS'.
(Other definitions for asps that I've seen before include "because of their venom?" , "Pass around the snakes" , "Pass (anag)" , "Poisonous creepers" , "poisonous things" .)