As of now, it is not possible to purchase iReal Pro on iOS 12 or lower.
There is a workaround but we cannot take any responsibility that it will work in every case.
We have had a number of users who succeeded.

Install the previous version of iTunes to your computer (or use an old computer) and purchase iReal Pro via the App Store.
Here is a link to previous iTunes versions: http://osxdaily.com/2017/10/09/get-itunes-12-6-3-with-app-store/
We are not aware of any changes to the iTunes library itself, but if you are cautious you could run a Time machine backup before you downgrade the iTunes app.

Update from a user (as at July 2020):
"The version of iTunes available at the link is no longer 12.6.3 but is now 12.6.5. 
The process works exactly as described. Also it is necessary to update the iTunes Library."

After you purchased it on your computer, log in to the App Store on your iPhone/iPad with the same Apple ID to install the last compatible version of iReal Pro. You might be able to claim a refund if there is a problem installing after purchase. (Please review Apple's information on refunds before you start as we are not able to issue refunds.)

The version of iReal Pro which is installed is an older version and (obviously) cannot be updated on your old device because of its old OS. Your App store purchase will be valid should you purchase a newer device in the future.

We have also had another user sign in to his Apple account using his wife's current model iPad, purchase iReal Pro under his own account, then download on his older iPad - iReal Pro listed in the Purchases section, it asked to confirm installing "the last compatible version of iReal Pro" which he did, then it installed.