Replacing the iPhone 13 screen will make Face ID unavailable and an error message will state "Unable to activate Face ID on this iPhone."
In view of the repair suppliers' dissatisfaction with this restriction, Apple decided to change its policy and plans to launch a software update that allows screen repairs without disabling Face ID.
In iPhone 13 series, Apple added a small microcontroller to pair the iPhone 13 with its display screen. When repairing the display screen, Apple's tools must be used to pair the microcontroller with the new screen, and independent repair shops cannot use these tools. Without this pairing process, replacing the iPhone 13 screen with a new one will result in the error message "Unable to activate Face ID on this iPhone."
The software update Apple plans to implement will remove the restriction that requires the microcontroller to be transferred to the new screen during repairs. So third-party repair shops will again be able to repair the screen without affecting the Face ID function. There is no news about when Apple will add this software updates for improvements, but iOS 15.2 is currently in Beta testing and it is expected to be introduced in iOS 15.2.