My iPad won’t update to iOS 13

1. The latest version of ipad OS is now ipadOS 14.3 rather than ipadOS 13.
2. Are you running an eligible device to upgrade? - To find out go to https://www.apple.com/uk/ipados/ipados-14/ and search at the bottom.
3. Follow the steps at If your iPhone, iPad or iPod touch won’t update - Apple Support

Your question suggests that you have iPad Air, iPad mini2 or mini3; these models of iPd can only be updated to iOS 12.5.

Apple ended major update support for these devices in September 2019. Whist they have since continued to receive “point” security updates, they 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 the most recent versions of iOS, you’ll need to consider replacement of your iPad with a newer or current model that supports iPadOS13/14.

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

What iPad?