Signal page with buzzer first (4)

I believe the answer is:
beep
'signal page' is the definition.
'beep' can be an answer for 'page' (I've seen this in another clue). I'm unsure of the 'signal' bit.
'with buzzer first' is the wordplay.
'with' is a charade indicator (letters next to each other).
'buzzer' becomes 'bee' (insect which buzzes).
'first' becomes 'p' (I can't explain this - if you can you should give a lot more credence to this answer).
'bee' next to 'p' is 'BEEP'.
Can you help me to learn more?
(Other definitions for beep that I've seen before include "Electronic warning sound" , "Toot" , "Short high-pitched sound from an electronic device" , "Warning signal" , "Electronic noise" .)
