Tory's beginning to irritate Speaker (6)
I believe the answer is:
tannoy
'speaker' is the definition.
(I know that tannoy is a type of speaker)
'tory's beginning to irritate' is the wordplay.
'beginning to' suggests taking the first letters.
'irritate' becomes 'annoy' (synonyms).
The first letter of 'torys' is 't'.
't'+'annoy'='TANNOY'
(Other definitions for tannoy that I've seen before include "Orator's amplifier" , "Public address system" , "Loudspeaker system" , "Speaker" , "Sound amplification system" .)