Clue: Fear of treater of nippers (perhaps nip too bad — ooh, nasty!) (12)
Answer: ODONTOPHOBIA
Explanation: Definition: Fear of treater of nippers (perhaps
***(nip too bad ooh)** [anag:*nasty*] 
*Chambers has odontophobia as "the fear of teeth", but odontophobia doesn't appear in my Collins or one-volume OED. However, the internet has several mentions of odontophobia as an alternative to dentophobia (also not in any of the dictionaries) meaning "fear of dentists", so the "treater of nippers" in the clue is a dentist, I guess.