Most of the time, an update to your carrier’s voicemail app or settings will cure the issue; however, it is important to confirm that your voicemail number is appropriately configured before proceeding any further.
Call your iPhone from another phone and try to leave yourself a voicemail. Go to the keypad and press and hold the number 1, or press the Call Voicemail button. This dials voicemail. Check if you have any missed messages. On the Voicemail screen, tap Greeting. Then change your greeting to either custom or default. If you have more than one

Change your iPhone voicemail greeting using the Phone app on your device. The Phone app is the one with the white phone icon in a green box. For many users, this icon is one of the four permanent apps on the bottom of the screen. Tap the Phone app icon to enter the phone application.
Just click the "Phone" App from the home screen of iPhone. You can press "1" or the "Voicemail" key to access to voicemail on AT&T phone. Note: T-Mobile users, tap on "Keypad" or press 123. Verizon users, press *86 instead of 1. And Sprint users, press 1. And then you can change the default voicemail on iPhone from different carriers.