Replacing existing doorbell with Wired Ring Doorbell

Replacing existing doorbell with Wired Ring Doorbell
I'm trying to replace my existing doorbell with a wired ring doorbell. I thought it was a simple case of taking off old, using the wires on new one, bingo! But I just realised my existing door bell does not have a separate chime but actually the burglar alarm control panel (keypad) is what chimes when the bell is pressed.

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