How can I transfer music from my iPod to my new iPhone

Here's what you need

• Update your iPhone or iPod touch to the latest version of iOS, iPad to the latest version of iPadOS, or Mac to the latest version of macOS. On a PC, make sure that you have the latest version of iTunes for Windows.
• Subscribe to Apple Music or iTunes Match.
• Sign in to all of your devices with the same Apple ID that you use with Apple Music or iTunes Match.
• Connect your devices to the Internet over a Wi-Fi or cellular network. On a Mac or PC, you can also connect to the Internet using Ethernet.

Apple Music availability varies by country and region. Learn what's available in your country or region.

Turn on Sync Library

With the latest version of iOS, iPadOS, and macOS, Sync Library is turned on by default. If you turned off Sync Library, you can turn it back on. Just follow the steps below for your device.

On your iPhone, iPad, or iPod touch

1. Go to Settings > Music.
2. Turn on Sync Library. If you don't subscribe to Apple Music or iTunes Match, you won’t see an option to turn on Sync Library.

If Sync Library is updating or turned off, you'll see a message at the top of the Library tab in the Apple Music app.

Unfortunately SravanKrA is wrong in this case.

Neither Apple Music or iTunes Match will extract music from an iPod Nano in any way. The iPod Nano has no connection to Sync its Library.

You will need to extract all the music from the Nano, import it into iTunes on a computer (Mac or PC) first and then you can choose to use iCloud Music library as explained above, or simply sync the music to the iPhone directly via USB cable.

See here: link-> Recover media from an iPod - Apple Community

then: link-> Use iTunes to sync your iPhone, iPad, or iPod with your computer - Apple Support

Note that Apple Music and iTunes match are subscription services and cost money to use. The direct USB method is free.