For one of my app, I need iOS 13 but my ipad Air is setted with ios 12.5.5. How can I update my iPad to ios 13 or more.

You’ll not be able to update your iPad to iPadOS13.

The first generation iPad Air, iPad mini2 and mini3 can only be updated to iOS 12.5.5.

Apple ended major update support for these models of iPad in September 2019 - although they since continue to receive “point” security updates - the most recent being released just recently. These devices cannot be updated to iPadOS 13 (or any later major versions of iPadOS) as the internal hardware does not meet the minimum technical requirements (CPU and RAM) for newer versions of iOS/iPadOS.

Some App developers have dropped support for iOS versions preceding iOS 13.x for technical reasons (often because APIs or software libraries upon which they rely have been updated in the new version of iPadOS, making their App incompatible with earlier versions). 

Whilst many App titles remain compatible with your iPad, if you want or need to access to Apps requiring more recent versions of iOS than your iPad can support, you’ll need to consider replacement of your iPad with a newer or current model that supports iPadOS15.

Sorry, I appreciate that this may not be what you were hoping to learn.

I hope this information provides clarity as to your available options - and the fundamental limitations of your iPad.

Hello ~ You need a newer device. You can go to upper black line and click on iPad to see your newer choices. If you are considering a second hand device please take a moment to read these:

Activation Lock for iPhone, iPad, and iPod touch - Apple Support

Also:

The All Too Common SAD Reality of Buying a Used iPad/iPhone

~Katana-San~

An unit running 12.5.5 isn't capable of 13 or above.

(211897)