You may need to have a payment method on file, even if the app you want to download is free.
Sign in to your Apple ID account page and edit / update your Apple ID details.
https://appleid.apple.com
On the Sidebar click Payment methods -> then tap Payments Methods and tap Manage payment method.
Or -> Change, add or remove Apple ID payment methods
Change, add or remove Apple ID payment methods – Apple Support (UK)
See also -> Payment methods you can use with your Apple ID
Payment methods you can use with your Apple ID – Apple Support (UK)
You can also use your Apple ID balance as payment method:
Add money to your Apple ID balance
Add money to your Apple ID balance – Apple Support (UK)
What you can buy with your Apple Gift Card or Apple ID balance
What you can buy with your Apple Gift Card or Apple ID balance – Apple Support (UK)
How to redeem your Apple Gift Card or App Store & iTunes gift card
How to redeem your Apple Gift Card or App Store & iTunes gift card – Apple Support (UK)