Sound system doesn't start to irritate (5)
I believe the answer is:
annoy
'to irritate' is the definition.
('annoy' can be a synonym of 'irritate')
'sound system doesn't start' is the wordplay.
'sound system' becomes 'tannoy' (I've seen this before).
'doesn't start' means to remove the first letter.
'tannoy' with its initial letter removed is 'ANNOY'.
(Other definitions for annoy that I've seen before include "Upset" , "be a nuisance" , "Anger" , "Irritate, nettle" , "Bother, irritate" .)