Anyone upset about party in Africa is a pest (9)
I believe the answer is:
annoyance
'pest' is the definition.
(pest can mean an annoying person)
'anyone upset about party in africa' is the wordplay.
'upset' indicates anagramming the letters.
'about' is an insertion indicator.
'party in africa' becomes 'anc' (African National Congress, South African party).
'anyone' anagrammed gives 'annoye'.
'annoye' enclosing 'anc' is 'ANNOYANCE'.
'is a' acts as a link.
(Other definitions for annoyance that I've seen before include "pest" , "Pain" , "Source of anger" , "trouble" , "Nuisance" .)