Your intercom may not work with your new doorbell at all, but you can get power from your main intercom unit inside and send that power through the wire to your outside doorbell.

First, locate the wire that comes from your old front doorbell and runs to into the main unit.

At your main unit inside, screw one wire that comes from the old intercom outside directly to the transformer next to the main unit inside the house. Then outside, find the other end of that same wire and hook up to the doorbell.

You are basically getting power from the old intercom transformer inside and sending that power outside to power the new doorbell.