Character giving a knowing look about a teetotaller (6)
I believe the answer is:
letter
'character' is the definition.
(I know that letter is a type of character)
'a knowing look about a teetotaller' is the wordplay.
'a knowing look' becomes 'leer' (I've seen this in another clue).
'about' indicates putting letters inside.
'a teetotaller' becomes 'tt' (abbreviation).
'leer' enclosing 'tt' is 'LETTER'.
'giving' is the link.
(Other definitions for letter that I've seen before include "he leases" , "Communication via the postman" , "who may offer terms to residents?" , "Epistle, missive" , "Written character - landlord" .)