I want to download the Apple Pay app

There is no app with the name "Apple Pay." There is a "Wallet" app that is use for Apple Pay and there are Settings for Apple Pay.

To set up Apple Pay, see: Set up Apple Pay - Apple Support

If your Wallet app is missing from your Home Screen be aware that apps can be removed from the Home Screen without being deleted. Go to the App Library (swipe left past your last Home Screen). From there you can touch and hold an app and slide it to the Home Screen.

If the Wallet app was deleted, see the following from Delete built-in Apple apps from your iPhone, iPad, or Apple Watch - Apple Support

Restore a built-in app that you deleted

1. On your iPhone, iPad, or Apple Watch, go to the App Store.
2. Search for the app. Make sure that you use the exact name of the app.
3. Tap the Redownload button .
4. Wait for the app to restore, then open it from your Home Screen.

Another reason for the Wallet not being visible is due to a restriction. Go to Settings and tap Screen Time, tap Content & Privacy Restrictions, tap Allowed Apps. Also see the following Apple Support article for more information: Use parental controls on your child's iPhone, iPad, and iPod touch - Apple Support

You mean you want to download the wallet app? There is no Apple Pay app. If you accidentally removed wallet from the home screen it can be found in the App Library on your device.