cellular still not working after update

Which Update are you referring to?

1. iOS update OR
2. Carrier Settings Update

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1. iOS Update (Recommended): Released by Apple Inc basically for improvements, security and bug fixes. My 10 years of experience says, it may not be the primary cause of any failure of Cellular Data, Calls & SMSs on your iPhone, if not updated
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2. Carrier Update (Required): Released by your Cellular Service provider (Carrier Update), affects your Outgoing / Incoming calls, SMS, Data etc..
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How to Update Carrier Settings

You can manually check for and install a carrier settings update with these steps: Make sure your device is connected to a Wi-Fi or cellular network. Tap Settings > General > About. If an update is available, you'll see an option to update your carrier settings.

Update your carrier settings on your iPhone or iPad - Apple Support

How to update iOS

Go to Settings > General > Software Update > Automatic Updates, then turn off AutomaticUpdates. At any time, you can check for and install software updates. Go to Settings > General > Software Update. The screen shows the currently installed version of iOS and whether an update is available.

Update iOS software on iPhone - Apple Support

Finding No service? --> If you see No Service or Searching on your iPhone or iPad ...