When you dial a number on a Blackberry OS 10 device like the Classic or the Z30, you hear the typcal "dialling" sound, also called DTMF. Unfortunately, there is no switch to turn that off.
The only way to do this is to switch your sound profile to "Silent" or "Vibrate", but that mutes any other notifications as well.
Here are the instructions to turn the dial pad tone off but still hearing other notifications:
Settings > Notifications
Make sure, the active profile is "Normal"
Under the Profiles heading, tap on "Normal"
On the "Normal" profile, toggle "Sound" off
Tap on "Customize App Notifications"
Tap on "Phone" and toggle "Sound" on
With that, you will hear the ring tone, but you will not hear the dial pad.
If you have other apps that should do sound notifications, e.g. Calendar, you have to go to "Customize App Notifications" > "Calendar" and set the Sound to on as well.