What do I need to do
Follow these instructions and phone prompts. When you get to new phone line or replacement choose replacement.
If your old phone is also with Republic Wireless, then you can do that at the time of activation
by using the activation instructions provided by @bocephous above.
If your old phone is with a different provider then you will need to first activate your new phone with a new phone number on Republic Wireless and then submit a Number Transfer request as outlined in this document