Apple Store is not letting me download

You can download free apps, but you may need to have a valid payment method on file, even if the app you want to download is free. 

You can have a credit card / debit card on file and an Apple Account balance.

If you have set your Apple Account balance as your default payment method, your default payment method will be used first by Apple when you need to make a payment.

Free apps has also In-app pruchase.

See -> Buy additional app features with in-app purchases and subscriptions

Buy additional app features with in-app purchases and subscriptions

See -> Add a payment method to your Apple ID

Add a payment method to your Apple ID – Apple Support (UK)

• If you want to change your card, you need to add first the new card, then remove the old card.
• or if you want to use your Apple Account balance, you need to set your Apple Account balance as your default payment.

See also -> Payment methods you can use with your Apple ID

Payment methods you can use with your Apple ID – Apple Support (UK)

fyi: Not all credit & debit cards seem to work with App Store / iTunes Store, try a different one, or preferably a credit card. If your card is not accepted as a paymenf method, you need to contact your bank.