How can i recover deleted voicemail on iPhone?

In the deleted voicemail box, assuming the message is still there, tap the message then tap the Red Trash can, which has a \ through it and it will be restored.

Contact your carrier, voicemail are stored on their servers. They might be able to recover it for you.

Please contact your carrier to see if they have a user site that would allow you to retrieve the voicemail.

You're welcome. Since this is a really important message, You might want to save it somewhere safe. Tap the message, then see the box at the top with an up arrow and send it to yourself and then save it as a file on a computer or someplace it can't be deleted.