Q: How can I download music from old phone to my new phone

Music is transferred (synced) using computer iTunes.

If the music was bought from iTunes music store, you can directly download (under Purchased) using the same Apple ID & password.

You can re download past purchase from iTunes for free using the same Apple ID they were originally purchased from.

Download your past purchases - Apple Support

Otherwise you need a computer running the latest version of iTunes in order to transfer music from the old iPhone to the new one.

If the song was purchased on iTunes and has since been withdrawn for some reason - you may not have access to it in iTunes -

If you ripped it from a source and have the original - you can import it as per usual and then sync it

The other option is to search method(s) of transferring a song from an iOS device to a USB stick and then importing that into iTunes to sync with the new device

See Recover your iTunes library from your iPod or iOS device.

tt2