Warning sign the Speaker's studied (3)
I believe the answer is:
red
'warning sign' is the definition.
(traffic lights)
'speaker's studied' is the wordplay.
'speaker's' shows a homophone (sound like).
'studied' becomes 'read' (to read a subject is to study it at university).
'read' is a homophone of 'RED'.
'the' acts as a link.
(Other definitions for red that I've seen before include "socialist?" , "14 -- breed of 4" , "- - poker: Kniphofia" , "Blood-coloured" , "Colour for a blusher" .)