Annoyed being listened to secretly (6)
I believe the answer is:
bugged
This clue is a double definition.
'annoyed' is the first definition.
(I've seen this in another clue)
'listened to secretly' is the second definition.
(bugging is covertly recording someone)
'being' acts as a link.
(Other definitions for bugged that I've seen before include "Fitted with illegal listening or recording device" , "Softly glowing" , "Of room, fitted with secret microphones" , "Irritated; planted concealed microphones" , "Fitted with hidden microphone for eavesdropping" .)