Story about teetotaller — right gossip! (7)
I believe the answer is:
tattler
'gossip' is the definition.
(thesaurus)
'story about teetotaller right' is the wordplay.
'story' becomes 'tale' ('tale' can be a synonym of 'story').
'about' means one lot of letters goes inside another.
'teetotaller' becomes 'tt' (abbreviation).
'right' becomes 'r' (common abbreviation).
'tale' going around 'tt' is 'tattle'.
'tattle'+'r'='TATTLER'
(Other definitions for tattler that I've seen before include "One who gossips" , "Chatterer" , "gossip" .)