1. In your current KakaoTalk, go to More Settings > Privacy > Kakao Account to create a Kakao account.
2. If you want to save your messages before verifying your new number, you have to back up your chat data in advance.
Go to More > Settings > Chats > Chat Backup and back up your chat history.
3. Delete and reinstall KakaoTalk, and verify your new phone number.
4. After verifying your new phone number, log in with your previous Kakao account and you will be able to continue using the KakaoTalk with your new number.
(If you already have a backed up chat data, you will be able to see a Restore page at this stage.)
* Log in with your Kakao account in your new KakaoTalk to restore the following information:
friends list, recommended friends list, blocked friends list, hidden friends list, sent/received items, KakaoTalk ID, profile picture and status message.
(Friends whose phone numbers are not saved in your contacts will be returned to their set name - nicknames cannot be saved.)