Annoyed, but different in the sack! (8)
I believe the answer is:
bothered
'annoyed' is the definition.
('bother' can be a synonym of 'annoy')
'different in the sack' is the wordplay.
'different' becomes 'other' ('other' can be similar in meaning to 'different').
'in the' means one lot of letters goes inside another.
'sack' becomes 'bed' ('in the sack' means 'in bed').
'other' put into 'bed' is 'BOTHERED'.
'but' acts as a link.
(Other definitions for bothered that I've seen before include "Disturbed" , "` `Bewithched, ... and bewildered' '" , "Old song: 'Bewitched, . . . . . . . . and bewildered'" , "Under stress" , "''Bewitched, ... and bewildered'' (song) (8)" .)