You can download iReal Pro on both iPhone and iPad from the App Store as long as you use the same Apple ID.
Open the App Store on your iPhone/iPad and look for iReal Pro to download it.

On iOS 13 & higher:
tap on Updates, then your account on the top right. Tap on Purchased/My Purchases and look for iReal Pro. It should be listed there if you previously purchased it.

Note: in case Apple charges you again, please contact them directly as we don't have access to billing and Apple IDs.

Older iOS versions information here.