I want my iPad software update to download app but it shows update iOS 13 version

On your device, tap:

Settings > General > Software Update.

1. If it says your device is up to date there is nothing more you can do. If apps you are trying to use say you need a higher iOS version, you will need to buy a newer device if you want to run those apps or features.

2. If it says an update is available you will only be given one update selection which will be the highest available iOS version supported by your device. Click on a link below for full instructions about how to update with wi-fi or 5G, or using a computer if you have storage or connectivity issues. If the update listed is not equal to or higher than the iOS version you need to use a feature, you again will need to buy newer equipment if you want to use that feature.

"Update your iPhone, iPad, or iPod touch" click here --> https://support.apple.com/HT204204

Or this video:

"How to update your iPhone or iPad" click here --> https://youtu.be/csJAEyvvruY

Upgrading/updating that iPad any farther will never, ever be possible.

If your iPad model has been stuck on iOS 10 for all of these past years, then it is possible you own an almost 9-year old, 2012 iPad 4th generation.

That iPad model cannot ever upgrade beyond iOS 10.3.3/10.3.4.

Your nearly 9-year old, iPad 4th gen model is too old, now.

Sorry.

Apple ended support for all 8-10-year old iOS devices nearly 5 years, ago, in 2016.

Third party app developers abandoned and stopped supporting these 8-10-year old iOS devices nearly 3 years, ago, in 2018.

There are, virtually, NO MORE third party apps available from the iOS App Store, any longer!

Third party compatible apps for such old devices are few and far between, now, in 2021.

This includes apps for both iOS 9 AND iOS 10 devices!

Simply put, a 4th gen iPad is too old and obsolete now.

Sorry, but this is the reality for ALL 8-10-year old AND OLDER iOS devices now. Especially now in 2021!

If you need/want an iPad with an up to date iPadOS with access to current, updated apps, then you really need to seriously consider a purchase of a new iPad model OR a much, MUCH “newer” and less expensive, refurbished or used iPad models, from better known, trusted Apple product/device retailers/resellers, some locally or from online, on the Web/Internet, capable of running the latest iPadOS versions.

There are PLENTY of less expensive, newer, older iPad models that can run the latest, current versions of iPadOS.

If you need OR ONLY able to purchase older, less expensive iPad models, look at older IPads from 2014 and later.

All of these older model iPads CAN run the latest iPadOS versions and the up and coming iPadOS 15.

2014, 9,7 inch screen iPad Air 2 models

2015, 7.9 inch screen iPad Mini 4 models

2015-2017, 12.9 inch screen iPad Pro models. ( 1st gen Pencil support )

2016, 9.7 inch screen iPad Pro models ( 1st gen Pencil support )

2017, 9.7 inch screen iPad 5th gen models

2018, 9.7 inch screen iPad 6th gen models (1st gen Pencil support )

2019, 10.2 inch screen iPad 7th gen models ( 1st gen Pencil support )

2020, 10.2 inch screen iPad 8th gen models. ( 1st gen Pencil support )

Get the largest internal data storage model you can afford as NO Apple iOS device has expandable storage.

I am sorry that you had to learn all of this, but this does not change any of the facts regarding these very old iOS devices.

Sorry & Best of Luck to You!