Transfer apps from old iPad to new iPad without a computer

Apps are not transferred between devices.

While data can be transferred from old to new device, only a “record” of installed Apps is transferred; the corresponding Apps are downloaded again, from the App Store, automatically by the target (new) device.

You should note that only Apps that are still available within the App Store can be downloaded and installed; any Apps that are no longer available, or Apps that have been withdrawn or retired, cannot be installed.

These support pages should get you started with setup of your new iPad - and the methods of transferring your data from old to new iPad:

Set up your iPhone, iPad or iPod touch – Apple Support

Transfer data from your previous iOS device to your new iPhone, iPad, or iPod touch - Apple Support

Use Quick Start to transfer data to a new iPhone, iPad or iPod touch – Apple Support

If the donor iPad, from which you are transferring your data precedes iOS12.4, QuickStart will not be available.

“Transfer” is rather a misnomer. In reality, your data and setup is merely cloned to the new device. Nothing is moved or removed from the original device.

An alternative is to restore either an iCloud or iTunes backup to the new device:

How to back up your iPhone, iPad and iPod touch – Apple Support

Restore your iPhone, iPad, or iPod touch from a backup - Apple Support

You can try Quickstart or iCloud:

https://support.apple.com/en-us/HT201269

Apps are usually downloaded directly.