Here's how you can recover previously deleted voice mails on your iPhone.
1. Tap on the Phone icon.
2. Tap on Voicemail.
3. Scroll down to Deleted Messages in your list of voice mail messages (it's at the bottom).
4. Tap on Deleted Messages.
5. Tap the voice mail message you want to undelete.
6. Tap the Undelete button.
Note that each carrier allows previously deleted voice mail messages to stick around for only a certain amount of time. So save the ones you want to keep as soon as possible after deleting them.
For more, see the original article at the link below.
How To Recover Deleted Voice Mail On An iPhone | App Advice