Clue: Standards of behaviour quite possibly better after extremists leave (9)
Answer: ETIQUETTE
Explanation: Standards of behaviour quite possibly better after extremists leave (9)
*(quite) + (b)**ETTE**(r) 
"Possibly" *is the anagram indicator, and* "after extremists leave" *indicates that we should remove the extremes (i.e the first and last (letters)) of the word *"better"