Privet cut down, surprisingly revealing snake (5)
I believe the answer is:
viper
'snake' is the definition.
(viper is a kind of snake)
'privet cut down surprisingly' is the wordplay.
'cut down' means to remove the last letter.
'surprisingly' indicates anagramming the letters.
'privet' with its final letter taken off is 'prive'.
'prive' anagrammed gives 'VIPER'.
'revealing' is the link.
(Other definitions for viper that I've seen before include "Venomous snake, person" , "crawler" , "Adder" , "treacherous type" , "Deadly-venomous snake" .)