Look, it’s the Speaker’s dog! (4)
I believe the answer is:
peek
'look' is the definition.
(peek can mean to look at quickly)
'the speaker's dog' is the wordplay.
'the speaker's' indicates a 'sounds like' (homophone) clue (as it might sound when spoken).
'dog' becomes 'peke' (short for Pekingese).
'peke' sounds like 'PEEK'.
'it's' acts as a link.
(Other definitions for peek that I've seen before include "Quick, sly look" , "Repeatedly look like this" , "Quick or furtive look" , "Sly look, peep" , "Take brief or surreptitious look" .)