1. Open iTunes on your computer and sign in with the same Apple ID you used to purchase the music.
2. Connect your new iPod to your computer.
3. Click on the "Device" icon in the top-left corner of iTunes.
4. Select "Summary" from the left pane.
5. Click on the "Restore Backup" button.
6. Select the backup that contains your music purchases and click on "Restore."
Restore purchases through iCloud:
1. Make sure that your new iPod is connected to a Wi-Fi network.
2. Open the "Settings" app on your iPod.
3. Tap on your Apple ID banner at the top of the screen.
4. Tap on "Media & Purchases."
5. Tap on "View Account."
6. Enter your Apple ID password.
7. Tap on "Purchased."
8. Select the music that you want to redownload and tap on the "Download" icon next to it.
Once the music has been downloaded to your iPod, you will be able to listen to it in the Music app.