My phone will not download any app

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

See -> If you can't make purchases or update apps, including download free apps, you need to update your payment method or add a new one. 

See the following Apple articles:

Payment methods you can use with your Apple ID

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

Add money to your Apple ID balance

Add money to your Apple Account balance – Apple Support (UK) 

If necessary, click here for more support and assistance.