Avoid background noise. Whether you have music playing in your office, or you’re sitting in a coffee shop, background noise can make it difficult for your customers to understand your greeting. Limit the noise around you when you leave your voicemail greeting.
Turning on Airplane mode then turning it back on again has worked for a few of the people I asked about voicemail issues, so it’s well worth trying.

7. Check for and install a Carrier Settings update. Open Settings → General → About → If there is an update, you will see a pop-up. → Tap Update.
When you get a voicemail, you can check your message from the notification on your phone. Swipe down from the top of the screen. Tap Voicemail ….You can call your voicemail service to check your messages. Open your device’s Phone app . At the bottom, tap Dialpad . Touch and hold 1. How do you listen to your voicemail from a different phone? Call your 10-digit wireless number. When you hear your voicemail greeting, press the * key to interrupt it. If you reach the main voicemail system greeting, enter your 10-digit wireless phone number, then interrupt your greeting by pressing the * key. Can I listen to my voicemail without setting it up?