How do I restore non apple apps from an old iPad to new

Generally speaking, app information is restored to your new iPad from the old one’s backup. However, the app code is retrieved from the App Store. So that means if you had an old app on the old iPad that is no longer supported, it will not be possible to use on the new iPad and will be absent.

Presumably you have used QuickStart to transfer Apps, settings and data from your old to new iPad - or have restored an existing iCloud or iTunes backup to the new device.

Apps are not directly transferred between devices. For Apps, the transfer process creates a record of the Apps that are installed on the donor iPad - and it is this record of installed Apps that is transferred to the target device. For Apps that are still available for download from the App Store, the corresponding Apps are automatically downloaded and installed from the App Store.

Not all Apps will necessarily continue to be available. Apps may have been removed or retired from the App Store by the respective App Developer. Some Apps may have been abandoned - and some may not be compatible with the new device. Where a compatible App is not available, you’ll not be able to transfer/install the App.