Celebrity avoiding area annoys unknown people (9)
I believe the answer is:
strangers
'unknown people' is the definition.
(people you don't know)
'celebrity avoiding area annoys' is the wordplay.
'celebrity' becomes 'star' (a star is a celebrity or famous person).
'avoiding' is a deletion indicator.
'area' becomes 'a' (maths abbreviation).
'annoys' becomes 'angers' (to annoy is to anger).
'star' with 'a' taken out is 'str'.
'str'+'angers'='STRANGERS'
(Other definitions for strangers that I've seen before include "People one doesn't know" , "Outsiders" , "Those we have not met" , "Foreigners" , "Aliens" .)