I just got a new iPhone and it won’t let me download new apps

When you tap get, you should see a bouncing button pointing to your power button. That is telling you to tap the power button twice in rapid succession and the app will download.

Go to Settings > Screen Time > Content & Privacy Restrictions > iTunes & App Store Purchases > Is Installing Apps marked Allow?

You need a valid payment method tied to your account and to be signed into the App Store. And the payment method needs to be issued in the country of the App Store you are using. Is it?

Are you getting any error message when you try to down an app?

See this link for more tips --> If you can’t download or update apps on your iPhone or iPad - Apple Support

konnie148 Said:

"I just got a new iPhone and it won’t let me download new apps: I got a new iPhone 12 mini from an iPhone 11. For some reason I can’t download new apps on my new phone."

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Incompatible, Perhaps?:

If it is not installing, then perhaps the Developer has yet to do their part in making it compatible. Once compatible, all should presumably install and work.

konnie148 Said:

"We are going to go to Verizon in the morning to see if they can fix it then if not we will go to apple. I’m signed into iTunes and iCloud. So I don’t why it’s not letting me download new apps, only apps I’ve previously downloaded"

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Verizon:

See what Verizon has to say on this. If you like, consider reporting back what they say, as it may help others for certain.

Note that sometimes, changes and updates, are made and installed, respectively. And when that happens, sometimes, things need to be caught up with by the Developer. I'm not so certain how Carrier services (i.e. messing) would be involved in this. So, mention to them about the Developer maybe having to catch up to an update.