I am unable to send or receive a text message from one particular person on my brand new iPad, but do receive and send them on my iPhone. How can I correct this

You must explicitly enable Text Message Forwarding for your iPad on your iPhone.

On your iPhone:

Settings > Messages > Text Message Forwarding - set to ON - and explicitly enable your iPad from the list of devices.

Also ensure that Messages in iCloud is enabled on both your iPhone and iPad:

Settings > [Your Name / AppleID] > Messages - set to ON

More information:

How to forward SMS/MMS text messages from your iPhone to your iPad, iPod touch or Mac - Apple Support

Fault finding if needed:

If you can't send or receive messages on your iPhone, iPad, or iPod touch - Apple Support

I hope you find this to helpful in resolving the issue.

In all cases, that I'm aware of, when you cannot successfully send or receive text messages (either iMessages or SMS) to a specific individual, the issue is on their end. The fact that you can send them successfully with other devices does post a bit of a mystery though.

Is this issue with iMessages or SMS text messages, or both? Have you contacted the recipient about this?

Does that person use something other than an iPhone (i.e. doesn’t have iMessage). You will need to open settings on the phone and set Messages to forward SMS messages to the iPad.

Setting app > Messages > Text Message Forwarding