Unable to install iOS 15.7.2 update

Try downloading it again.

1.

First, to delete the update, go to:

Settings -> General -> iPhone Storage

Find the iOS update, tap and delete it.

After that, restart your iPhone.

2.

Now you go to:

Settings -> Screen & Brightness -> Auto Lock

Set to Never. This is to prevent your iPhone from locking while the update is downloading. It's not VERY necessary, but I personally found updates to work better when the screen is on.

3.

Now you connect your iPhone to a charger, and make sure you are connected to WiFi, then go to:

Settings -> General -> Software Updates, and choose to download again. Leave your phone with the screen on until it says Install.

Remember to set Auto Lock back to lock automatically, when your iPhone is updated.

Assuming you're trying to update your device wirelessly, and bearing in mind that to perform such a procedure you need to connect your device to a reliable and fast Wifi Network with Internet access (no cellular data, unless you use a 5G network, no personal hotspot on your device, no VPN connections are admitted, no Low Power Mode enabled, and I suggest that you keep the device plugged into power during the whole update process), read this support article:--> If your iPhone, iPad or iPod touch won’t update (if you don't have a reliable and fast wifi network, "borrow" one from your relatives/friends/neighbors).

Also, make sure your device is NOT running a Beta operating system version. Should be this case, you need to remove it before installing any official iOS/iPadOS releases, as per these instructions:--> How to uninstall iOS or iPadOS beta software - Apple Support.

DO NOT forget to create a full backup of your device before updating its operating system, and keep in mind that, depending on the available storage on your device and/or on your wifi network speed, it might take 30-60 minutes to complete the entire update process.

If the issue persists or if the iOS version currently running on your device is very old , try to update it via computer (if you don't have a computer borrow one from your friends/neighbors, or ask for help at an Apple Store or Authorized Service Provider), then learn how to update your device manually if you're using a Mac with macOS Catalina or later, or if you're using a Mac with macOS Mojave or earlier or a Windows PC.

If you still get no help, contact Apple Support directly, using this link:--> Get Support

Regards

Giulio

Have you tried to restart your phone and try again?

Try updating using your computer instead of over the air.

Do you have any profiles installed here:

Settings -> General -> VPN & Device Management

Or do you have access to a computer so you can update there?