A Greek character’s a pest (5)
I believe the answer is:
aphis
'a pest' is the definition.
(I've seen this before)
'a greek character's' is the wordplay.
'greek character's' becomes 'phis' (letter from the Greek alphabet).
'a'+'phis'='APHIS'
(Other definitions for aphis that I've seen before include "Plant louse" , "Small insect" , "sucker?" , "Sap-sucking garden pest" , "Greenfly" .)