Don’t start to draw breath at snake (3)
I believe the answer is:
asp
'snake' is the definition.
(asp is a kind of snake)
I don't understand the remainder of the clue.
Can you help me to learn more?
(Other definitions for asp that I've seen before include "Cleopatra's poisoner" , "creeper" , "Cold-blooded killer" , "Small poisonous snake" , "Cleopatra-killing snake" .)