Quick to give cue (6)
I believe the answer is:
prompt
I believe this clue is a double definition.
'quick' is the first definition.
(I know that quick can be written as prompt)
'give cue' is the second definition.
(prompt can mean to give someone a cue)
'to' acts as a link.
(Other definitions for prompt that I've seen before include "Quick - cue" , "With little or no delay" , "Cue given to a performer" , "Give cue to forgetful actor" , "Arriving on time" .)