Seems Apple requires you to have a payment method in your account for the first time you log-in to the App Store or iTunes with your Apple ID, even if you are only downloading free apps.
Payment methods that you can use with your Apple ID:
(Scroll down to find your country)
Payment methods that you can use with your Apple ID – Apple Support
How to:
Change, add, or remove Apple ID payment methods - Apple Support
After you have used the App Store and iTunes for the first time, it is possible to remove the payment method.
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Re: Already previously had the app on my phone
If you can’t download or update apps on your iPhone or iPad – Apple Support
Wondering if you have changed / updated your Apple ID or Apple ID password in the meantime:
What to do after you've changed your Apple ID or password – Apple Support
All the best :-)