Once recording is completed, hit Tap to stop recording. Your recording will be saved and displayed as Custom greeting. To listen to your greeting press Play button.
You will be asked to delete your current Voicemail greeting. Click on the ‘Yes’ button that appears on the screen if you want to remove that. You can save your new recorded Voicemail greeting or can use the default recorded option. Wait and hear the new Voicemail greeting message that the instructions speak out. If you want to keep that recording as your Voicemail greeting, then save it. Or you can re-record the message to get a different greeting.

Some cell phone service providers allow users to access their voicemail accounts via external methods such as landlines, and those users could keep the voicemail greetings updated in the absence of cellular and internet service.
Enter a name for the new greeting and then tap Save. Change your greeting. To use a greeting that you've already recorded or switch back to the default greeting: On your iPhone or iPad, open the Voice app . At the top left, tap Menu Settings. In the Voicemail section, tap Voicemail greeting.