Another worth considering trick is to remove all the old voicemails that are consuming the storage and creating multiple dilemmas like this. To delete the voicemail here are the steps, Open the Phone app. Tap on Voicemail at the bottom tab. Then tap on Edit at the top-right screen. Select All the Voicemails and at last tap Delete.
3. Once there, tap on "Greeting" in the top-left corner. Your iPhone will take a few moments to fetch and load your current voicemail greeting, which you can play using the controls in the middle of the page.

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.
In the Voicemail section, tap Voicemail greeting. Tap Record a greeting. Tap Record . Record your greeting and when you’re done, tap Stop . Choose what you want to do with the recording: To listen to the recording, tap Play . To replace the recording, tap Redo. To save the recording, tap Save. Enter a name for the new greeting and tap Save.