A fan of the dentist? (9)
I believe the answer is:
extractor
I believe this clue is a double definition.
'a fan' is the first definition.
(I've seen this before)
'dentist?' is the second definition.
(I've seen this before)
'of the' acts as a link.
(Other definitions for extractor that I've seen before include "dentist" , "Juice-maker" , "Variety of fan" , "Device for removing air from a space" , "Eg, kitchen fan" .)