how do I retrieve a deleted app on a iPad 3rd generation?

At this late timeframe, this may no longer be possible.

You can open the iOS App Store and in the lower menu under purchases, tap purchases, search for the name of the deleted app and see if the older, compatible version will download back to that iPad.

If this is a fail.

There is another last thing you can try/attempt, if you need older versions of apps.

If you own much newer iOS device that can run either iOS 12 and.or iOS/iPadOS 13 and later, you can install the most recent app/s onto that more recent iOS device.

Then go back to your older iPad, open the iOS App Store, go to the Purchases section of the store app, search for the app/s you wish to try and download to that older iPad and see if an older version of the app is allowed to be downloaded/installed to that older iPad.

These newer iOS/iPadOS devices must use your same Apple ID user account and password as the older device you ard trying to get an older app for.

If still NO joy, if this is app was an Internet Website-based app, your only option is to use the app's actual Website, now.

Failing all of that OR IF NO joy, then there is nothing more to be done.

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!

AND, NO WAY to initially install any older, compatible, third party apps into this old iPad.

NO MORE SUPPORT! NO MORE APPS!

AND, that 5-year old default iOS Safari Web browser is too old, not secure and not safe to use to access the Internet, any longer.

There are virtually NO MORE third party Web browsers left for 8-10 year old iPads!

Available and more popular third party Web browser choices are GONE, now!

If you must use these old iPad models, here is what is left for still updated Web browsers.

Pickins’ are slim, now!

ALook Web browser ( A fairly new Web browser primarily designed for old iOS device versions, but is still available to newer iOS/iPadOS devices, as well ) I recommend this “new-ish” Web browser for old iPad models.

Dolphin Web browser

Maxthon Web browser

TOR private browser

TOR + VPN private browser

Turbo VPN private browser

This is pretty much it for iOS 9/10 compatible device, up to date, third party Web browsers today, in 2021.

Simply and bluntly put, a nearly 9-1/2-year old, 3rd 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!

Sorry.

It's 2021 now!

You may want 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, below, 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 )

2017,10.5 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!

If you decide to go down the path of purchasing used, secondhand Apple devices, here is how to avoid purchasing an Apple iOS/iPadOS device with user activation lock, in the future.

If you purchase any iPad, or any Apple iOS device, for that matter, used/second hand, online, or even in-person, make sure this iPad does NOT have user activation lock and has been properly reset for sale.

A properly reset for sale iPad should initially power up to an animated, multi-language “Welcome” screen.

DO NOT take the iPad seller's word that this iPad is user activation lock free,

We have seen plenty of used iOS device purchasers get scammed.

User Activation Lock can never be bypasss, circumvented or worked around IF there is no correct previous/original user information to be able to do so.

Apple doesn't get involved with ANY user activation locked, used/second-hand sold devices, either.

So, buyer beware.

If purchasing a used device in-person, power the iPad ON

If the iPad DOES NOT display the initial animated, multi-language “Welcome” screen, then pass on purchasing this iPad.

If the iPad powers up to any other screen, then forget purchasing this iPad.

You cannot trust that the seller actually has the correct needed info to properly reset the iPad back to factory settings right then and there before the actual purchase and exchange of money for the iPad, in question.

Pass on the device!

If you are purchasing this used iPad online ask the seller to provide multiple images, either online or be sent to you via email, showing this animated, multi-language “Welcome” screen of the interested in purchasing iPad model.

Even better, ask for a short video be sent to you showing this animated, multi-language “Welcome” screen, in action and in its entirety, posted to the online ad or emailed to you.

If the online iPad seller refuses any of these requests, pass on the iPad. DO NOT buy!

Good Luck to You!