At this point, we can’t be exactly sure why your iPhone won’t play voicemails. The voicemail you play in the Phone app on your iPhone is called Visual Voicemail, which downloads your voicemails from your carrier in the form of little audio files, similar to the music files you listen to inside the Music app.
These settings are based on Carrier provider, so you can use these steps on other mobile platforms and services. you can ask your questions that are in your mind in the comment section.

If your carrier supports the iPhone voicemail feature, you can retrieve and listen to your voicemail right from within the “Phone” app and call your contacts back by simply tapping their messages. That type of functionality is pretty neat and useful, because it saves you actual time. If not supported by your carrier, you will not be able to see the visual overview of your voicemail inbox and use any of the related features. Tapping the “Voicemail” tab in your “Phone” app will simply call the number associated with your voicemail box. So let’s get going with creating our custom voicemail greeting on iPhone! How to record your own Voicemail on iPhone Phone → Voicemail → Greeting → Custom → Record → Save
5. Your voicemail will walk you through the setup process, including recording your personal greeting (the message that plays when you receive a call that goes to voicemail) and possibly your voice signature (your name, spoken by you into the recording).