I updated iOS 15.5 but when installing appear to me an error occurred for iPad Air 2

Whether or not you are able to update any iPad to a newer version of iOS/iPadOS will be dictated by the iPad model - and the currently installed version of iOS. You can find this information here:

Settings > General > About

Not sure which iPad you have? Identify your iPad model.

Here is a list of the highest version of iOS supported by the older models of iPad (for simplicity - “generations” are shortened to a number) that are restricted in their ability to be updated:

iPad1 - iOS 5.1.1

iPad2, iPad3 and iPad mini1 - iOS 9.3.5 (WiFi Only models), iOS 9.3.6 (WiFi & Cellular)

iPad4 - iOS 10.3.3 (WiFi Only), iOS 10.3.4 (WiFi & Cellular)

iPad Air1, iPad mini2 and iPad mini3 - iOS 12.5.5

Newer models, not appearing in this list, are all able to be updated to the current version, iPadOS 15.5

If your iPad is capable of being updated to a more recent version of iOS/iPadOS than is currently installed, these support pages outline both the available methods by which the update can be performed - and troubleshooting should you experience difficulties:

Update your iPhone, iPad or iPod touch – Apple Support

If you can't update or restore your iPhone, iPad or iPod touch – Apple Support

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

iOS update and restore errors – Apple Support

Be aware that while an iPad may be capable of update, it may be too far behind the current version to be updated directly from iPad settings. In such circumstances you will likely need to use a computer to perform the update. You will need access to either a PC (with iTunes installed) or a Mac (with iTunes or Finder - as appropriate for the installed version of MacOS). Ensure that your installed version of iTunes has been updated to the most recent version; the essential device drivers are included.

Download and use iTunes for Windows – Apple Support

Update to the latest version of iTunes – Apple Support

Update software on iPhone, iPad or iPod touch in iTunes on PC - Apple Support

If you have a beta profile installed, ensure this has been removed from your iPad - as, otherwise, installation of production software updates may be inhibited. This support page provides the necessary information to remove the beta from your iPad:

How to uninstall iOS beta software - Apple Support

You should note that for your iPad to install an available update, its battery must be charged to at least 50% capacity - and/or be connected to its Power Adapter. Similarly, the iPad can only be updated over a standard WiFi connection - or be updated by a PC or Mac using iTunes or Finder - over a USB connection.

You give no details of the error that you see.

There are known issues with update of some iPad models (e.g., some models of iPad Pro) to iPadOS 15.x. Do you have a WiFi Only, or WiFi+Cellular model of iPad?

For affected WiFi+Cellular models of iPad, many are reporting that removal of the SIM tray from the iPad will allow the verification and installation processes to successfully compete. Other reports suggest that installing a SIM card (whether active or not) also permits the update process to complete.

You may need to restart the update process, but removing the SIM tray from the iPad is simple and costs nothing to try.

Remove or switch the SIM card in your iPhone - Apple Support

If you have a WiFi Only model, the current workaround is to remove the iPad Passcode - and then re-try the installation process. This has also been observed to resolve issues with installing/verifying the update on WiFi+Cellular models.

Be aware that removing the iPad Passcode has implications for any payment methods registered for ApplePay from iPad - and your Keychain (that includes your saved passwords). Assuming that you have other devices (such as an iPhone), your Keychain will remain preserved in iCloud - and can be easily re-synchronised with your iPad via iCloud. Payment cards registered for ApplePay will need to be manually re-added after the update.

Assuming you're trying to update your device wirelessly, and bearing in mind that to perform such a procedure you need to connect your device to a reliable and fast Wifi Network with Internet access (no cellular data, unless you use a 5G network, no personal hotspot on your device, no VPN connections are admitted, no Low Power Mode enabled, and I suggest that you keep the device plugged into power during the whole update process), read this support article:--> If your iPhone, iPad or iPod touch won’t update

Also, make sure your device is NOT running a Beta operating system version. Should be this case, you need to remove it before installing any official iOS/iPadOS releases, as per these instructions:--> How to uninstall iOS or iPadOS beta software - Apple Support.

DO NOT forget to create a full backup of your device before updating its operating system, and keep in mind that, depending on the available storage on your device and/or on your wifi network speed, it might take 30-60 minutes to complete the entire update process.

If the issue persists or if the iOS version currently running on your device is very old, try to update it via computer (if you don't have a computer borrow one from your friends/neighbors, or ask for help at an Apple Store or Authorized Service Provider), then learn how to update your device manually if you're using a Mac with macOS Catalina or later, or if you're using a Mac with macOS Mojave or earlier or a Windows PC.

If you still get no help, contact Apple Support directly, using this link:--> Get Support

Regards

Giulio

Try the suggested workaround - by removing the SIM tray from your iPad, and/or inserting a SIM card.

Otherwise, full troubleshooting steps are included within my initial reply.