Read out letter that's prompt (3)
I believe the answer is:
cue
'prompt' is the definition.
('cue' can be a synonym of 'prompt')
'read out letter' is the wordplay.
'read out' shows a homophone (sound like).
'letter' becomes 'q'.
'q' sounds like 'CUE'.
'that's' acts as a link.
(Other definitions for cue that I've seen before include "Signal to players" , "Used in snooker and on stage" , "Tapering stick used by snooker player" , "Actor's signal" , "Hint, prompt" .)