You will need to access the voicemail menu of your recipient for deleting or re-recording your voicemail. Try pressing * or # on the dial pad to access the menu. This works for both mobile phones and landlines unless the recipient has changed the options.
Website: https://shoretelcommunity.force.com/s/article/How-to-Record-and-Change-Your-Voicemail-Greeting

The next step is very important and you need to get it right. Say your phone number two times very slowly so the person has enough time to write down your number as they are listening to your message the first time.
Increase the odds of getting a call back by mentally composing your message before each call. And remember, people hate it when callers state their name and phone number too quickly in voice mail messages – no one wants to listen to a message ten times to comprehend simple information. Begin by saying your name and company (if applicable). Then assume the person you’re calling doesn't have your number, so say your phone number twice. If your name is at all unusual, spell it the first time you say your phone number. Talk slowly like you were writing it down yourself. The second time you say your phone number, you can say it at your normal rate of speech. A gracious phone message is no longer than 30 – 45 seconds. Be pleasant, but also get right to the point. Keep your voice mail message to two points maximum. If you need to share more information, then say you will send an e-mail message with the rest of the details. Leave a specific message. There’s nothing more frustrating than a voice mail that says, “Hi, it’s me. Call when you can!” Even if you’re just calling to say “Hi”, tell them that in your message. End on a high note! You don’t necessarily need to say “Goodbye” at the end of a voice mail, because you didn’t really talk to anyone. Instead, try something like, “Look forward to talking* with you!”