Eavesdropper (5)
I believe the answer is:
snoop
'eavesdropper' is the definition.
(synonyms)
This is all the clue.
(Other definitions for snoop that I've seen before include "Furtively investigate" , "Informally, pry inquisitively" , "Investigate; pry" , "-- Dogg, US rapper; spy" , "Furtively look around" .)