Updates are free. The App Store keeps iReal Pro up to date automatically. To update by hand, see Apple's guide: How to manually update apps from the App Store.
The latest version of iReal Pro requires iOS 16 or later. If your device can't run iOS 16, you can still use the last version of iReal Pro that supports it, see Install iReal Pro on an iPhone or iPad with older iOS.
If the Update button keeps spinning in the App Store, back up your songs first (email a copy to yourself), delete iReal Pro, then reinstall it from the App Store.