First look at the Support article: If you see No Service or Searching on your iPhone or iPad - Apple Support
Go through the various suggestions in the support article above but if they don't help, and your network carrier can't help, then you may need to contact Apple Support for further investigation.
Then try a Forced restart Force restart iPhone – Apple Support (UK)
If no better, and hardware can fail during an update if it was already on the way out, you should arrange a repair iPhone Service & Repair - Apple Support
Or
Contact - Official Apple Support
Anything other than Screen or Battery may be a replacement phone and the price is in the article under "Other damage". If on warranty it should be covered if there is no evidence of accidental damage.
See also: Get your iPhone, iPad, or iPod touch ready for service - Apple Support