Why is the update option not showing in my settings on iPhone 7 Plus

It should:

How to update to iOS 15 or iPadOS 15 - Official Apple Support

The first (and simplest) thing to try if something isn’t working right is to restart your iPhone.

Restart your iPhone - Apple Support

Thejealousguy Said:

"Why is the update option not showing in my settings on iPhone 7 Plus"

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Why the Issue?: Perhaps there is an error connecting to Apple's servers?

To Check for Updates:

Use a Computer and Ethernet:

Start with attempting an update through use of a computer. If you cannot use Wi-Fi, then use Ethernet.  Go Here: Update your iPhone Using a Computer - User Tip. On the computer, you would connect it through Ethernet, going directly into your router. For a Mac (or PC) that does not have Ethernet, this would be the adapter to use: Belkin USB-C to Gigabit Ethernet Adapter - Apple. If you get the same error, the model is likely just not compatible.