Icon doesn’t change on main screen when personalized.
It might be helpful if you mention what device and iOS version you’re using. 
For instance, it works fine on my iPhone 14 Pro with iOS 17.2.1 and my old iPhone 8 with iOS 16.2.
I am using an iPhone 15 pro max with the latest software version.
I’ve run into this issue occasionally, not just with Clear but with any app that offers icon customization. It seems to be a problem with the way iOS handles icon changes. A quick reboot has always fixed it for me.
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I’ve also seen this, but always as an iOS issue- when this happens, try changing an icon on another app to see if it’s an issue with Clear specifically, or an issue with the system