Most of the time this error is caused by the connectivity of your phone to a cellular network or WiFi connection. The easiest way for solving this issue is by turning the Airplane Mode ON. On your main screen of the phone, you can swap down the notification bar and tap on the Airplane Mode option. Once it is ON all the connectivity to your phone will be turned off. You can wait for 30 seconds and then turn it back OFF by using the same method. This option can vary depending on the device you are using. For some devices, you need to go to settings or use the power button on the phone to get to Airplane Mode. After applying this method, you can now try updating or setting up the voicemail greeting on your phone.
Pro tip: You can double-check to see if voicemail is set up on your iPhone by dialing and calling your own phone number in the Keypad of the Phone app, or by calling your iPhone using another phone.

If resetting your Networks Settings doesn't work, the Apple forums suggest enabling Airplane mode for 30 seconds to return to Visual Voicemail. I have personally experienced the "Call Voicemail" issue every time I have updated to the newest iOS 11 beta and reboot my phone. After two attempts, the Airplane suggestion worked and returned my Voicemail back to normal, where I can read a transcript or listen to an individual voicemail directly from my iPhone. Here's how to quickly enable and disable Airplane mode: Swipe up from the bottom of your display anywhere on the Home screen. Tap the airplane icon. Wait 30 seconds then tap the airplane icon again.
That way you'll get to know exactly what other people hear when they call your phone and one last thing I wanted to show you. If you don't see that play on record option on the bottom, you don't have visual voicemail. Set up on your phone and that's through your provider. So if you have at and T sprint T-Mobile or any other provider, you need to have visual voicemail.