Hi Leviathanliv,
Welcome to Apple Support Communities. We understand that you're having an issue with a previously purchased ring tone not working on your new iPhone. We'd like to help.
Is this issue isolated to this one ringtone or are other items not downloading as expected as well? What happens when you try to redownload from your purchases? Does the link to Download All continue to stay there or does it disappear for a bit? Is this Ringtone still available in the iTunes Store? Let us know.
In the meantime, let's have you close the iTunes Store app and restart your iPhone. These steps may seem small but they are helpful in situations like this:
How to close an app
You should close an app only if it’s unresponsive. The way you close an app depends on the type of device that you have. Find your iPhone or iPod touch model below, then follow the steps. Or learn how to close an app on your iPad.
iPhone X and later
1. From the Home Screen, swipe up from the bottom of the screen and pause in the middle of the screen.
2. Swipe right or left to find the app that you want to close.
3. Swipe up on the app's preview to close the app.

Restart your iPhone
Learn how to turn your iPhone off, then back on.
How to restart your iPhone X, 11, 12, 13, or later
1. Press and hold either volume button and the side button until the power-off slider appears.

2. Drag the slider, then wait 30 seconds for your device to turn off. If your device is frozen or unresponsive, force restart your device.
3. To turn your device back on, press and hold the side button (on the right side of your iPhone) until you see the Apple logo.
Let us know how that goes.
Cheers!