How do I get a new serial number for my replaced iPhone to update iOS?

Serial Number has nothing to do with iOS version/update.

If it is an iPhone X model (as showing in your products list), bear in mind that it supports iOS 16.7.10, no futher because of CPU/RAM limits.

Specifically:

Assuming you're trying to update your device wirelessly (Settings>General>Software Update), 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 (from your product list, it seems that the device is still running the old iOS 14), 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:--> Contact Apple for support and service

Regards

Giulio

"How do I get a new serial number for my replaced iPhone to update iOS?: My iPhone serial number as they said has been replaced how do I get a new serial number for it in other to update my iOS"

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Updating your iPhone:

iOS 18.3.2 is the latest available update. So, try updating to it. If you cannot not do so on the iPhone itself, then try using a computer. Use my User Tip: Update your iPhone Using a Computer - User Tip. If any updates are available, they will install, sure enough. IMPORTANT: If you have an option to update, however, then be certain you backup your iPhone first. That way, you will have something to restore your iPhone from should anything go wrong with the update.

Confirm your Device:

Having been given a new iPhone, make sure you are signed in to your Apple Account. Perform as instructed here: Check your Apple ID Device List to See where you're Signed in - Apple Support. 

Your question isn't entirely clear.

If what you're trying to say is that you went to Check Your Service and Support Coverage - Apple Support

and it says that it has been 'replaced', what that means is that the device itself was replaced by Apple because it was defective or was reported lost or stolen.

If that's what you meant, that device is unsupported. There is no warranty and Apple will not provide paid out of warranty service or support for it.