Verification requirements

Apple requiring a payment method, even for free apps, is not an uncommon observation. Some possible reasons are outlined in the links below such as outstanding balance, an issue with a payment method you have currently entered, or ongoing subscriptions. You can try to set up your account without a payment method but you may find there is no option other than to enter a valid payment method to satisfy Apple's requirement. If the item is free you will not be charged. You can also later remove the payment method and see if it only needs to be there temporarily.

If you can’t download or update apps on your iPhone or iPad - https://support.apple.com/HT207165

- "You might need to have a payment method on file, even if the app that you want to download is free." My interpretation of this in the context in which it has been presented is if you have something else on your account that requires a payment method, such as a subscription, and your current payment method is not working then Apple won't let you download even free things until you fix the payment method. This is explained in this document, 'If your payment method is declined in the App Store or iTunes Store' - https://support.apple.com/HT203005

Create or use your Apple ID without a payment method - https://support.apple.com/HT204034

- "You can remove payment methods from your existing Apple ID after you sign in to the App Store, iTunes Store, or Apple Books. You won't be asked for a payment method again until you make a purchase." One interpretation of this is if you want to "get" anything you must have a accepted payment form (e.g., card) on record. BUT: I download only free items and have never had to enter a card so I read this as instead meaning if you get something you truly "purchase" and actually costs money.

If you can't remove your last payment method or use no payment method with your Apple ID - https://support.apple.com/HT203905

- " if you're using an existing Apple ID with the App Store for the first time, you must provide payment information."

Also:

How App Store and iTunes Store purchases are billed - https://support.apple.com/HT201359

Some purchases aren’t charged to your Apple ID balance

- You can’t charge gifts to your Apple ID balance. If you send a gift or gift card, your primary payment method is charged.

- Some subscriptions might not be charged to your Apple ID balance.

If you still have problems Click here --> https://support.apple.com/choose-country-region/media-services Select your country, then a product. If you don't see one that handles your issue then keep experimenting with selections until you reach one that gets you a chat session or a telephone call and get the representative to redirect you.

or:

Contact Apple for support and service --> "See a list of Apple phone numbers around the world." - https://support.apple.com/HT201232

The resolution to this issue is often making sure you have entered a credit card or other valid method of payment even if you don't plan on needing to use it.

If there is an option to select "Review" or "Continue", select that and enter valid payment information if required. If there's problems doing this:

Tap: Settings > [your name at the top] > Media & Purchases > View Account > Review Apple ID.

More things to try in this 2018 post by Urquhart1244 marked Apple Recommended:

https://discussions.apple.com/thread/8434425?answerId=33542414022#33542414022

Payment methods that you can use with your Apple ID - https://support.apple.com/HT202631