Set up new phone

If you mean cellular service, then it has nothing to do with transferring data to the new iPhone.

If you have not yet set up the new iPhone, it should prompt you during setup to transfer the data from a previous iPhone. Just follow the onscreen steps.

click here ➜ Set up your iPhone or iPad - Apple Support

If it has already been set-up, then you will have to restore it factory settings and set it up again.

click here ➜ Restore your iPhone, iPad, or iPod to factory settings - Apple Support

My old iPhone 11 no longer has service

Does this mean that the iPhone 11 is not working at all, or something else?

Do you have a recent backup of the iPhone 11?