How can I install update without having cellular data connection? It will not install update on WiFi. Phone says can not connect to cellular data until update is complete.

1.

Phone says can not connect to cellular data until update is complete.

See these Apple articles below:

If you see No Service or Searching on your iPhone or iPad

If you see No Service or Searching on your iPhone or iPad - Apple Support

Manually update your carrier settings on your iPhone or iPad

Manually update your carrier settings on your iPhone or iPad - Apple Support

Update your network provider settings manually on your iPhone or iPad

Update your network provider settings manually on your iPhone or iPad – Apple Support (UK)

2.

Check iPhone type & iOS version -> Go to: Settings -> General -> About.

If your iPhone is eligible for an update, you can check by reading this Apple article:

iPhone models compatible with iOS 15.6.1

iPhone models compatible with iOS 15.5 – Apple Support (UK)

Then go to: Settings -> General -> Software Update

See the following Apple articles:

Update your iPhone, iPad, or iPod touch

Update your iPhone, iPad, or iPod touch - Apple Support (IN)

If your iPhone, iPad or iPod touch won’t update

If your iPhone, iPad, or iPod touch won't update - Apple Support

You can do the update via PC, see this Apple article: Update software on iPhone, iPad or iPod touch in iTunes on PC

Update software on iPhone, iPad or iPod touch in iTunes on PC – Apple Support (UK)

If you have a Mac see this Apple article: Update your iPhone, iPad, or iPod touch with the Finder

Update your iPhone, iPad, or iPod touch with the Finder - Apple Support

You need about 6 GB device storage and good Service & Wi-Fi.

If they are On, turn Off Hotspot & VPN.