Prompt car starts on way to read speech (7)
I believe the answer is:
autocue
'prompt car starts' is the definition.
'autocue' can be an answer for 'prompt'. I am not certain of the 'car starts' bit.
'on way to read speech' is the wordplay.
'on' means one lot of letters go next to another.
'way to read' becomes 'auto' (I can't explain this - if you can you should give a lot more credence to this answer).
'speech' becomes 'cue' (cue is a kind of speech).
'auto' put next to 'cue' is 'AUTOCUE'.
Can you help me to learn more?
(Other definitions for autocue that I've seen before include "TV signal" , "speaking aid" , "Vocal prompter" , "TV prompt device" , "Speaker's aid" .)