First, you need to make sure both your old and new iPhones are connected to Wi-Fi. Then, you have to ensure your Apple Watch and iPhone have at least 50% battery charge.
Update your old phone as well as your Apple Watch to the latest version of iOS.
Check your Health and Activity settings. iCloud doesn't store your data, so you may need to back it up and encrypt it.
Back up your old iPhone.
Set up your new phone.