To be inquisitive about a note to a teetotaller seems fair (6)
I believe the answer is:
pretty
'fair' is the definition.
(I've seen this before)
'to be inquisitive about a note to a teetotaller' is the wordplay.
'to be inquisitive' becomes 'pry' (I've seen this in another clue).
'about' is an insertion indicator.
'a note' becomes 'e' (musical note).
'to a teetotaller' becomes 'tt' (abbreviation).
'e'+'tt'='ett'
'pry' going around 'ett' is 'PRETTY'.
'seems' is the link.
(Other definitions for pretty that I've seen before include "like a kettle of fish" , "Attractive in delicate way" , "Attractive, beautiful" , "Somewhat - attractive" , "Reasonably" .)