Unable to send SMS messages on new iPad Air 4

In order to send SMS messages from an iPad you would also need to have an iPhone; the iPad can then send the messages through the iPhone. SMS messages require a text messaging plan with a cellular carrier and that requires a phone. If you have an iPhone, see instructions in How to forward SMS/MMS text messages from your iPhone to your iPad, iPod touch or Mac - Apple Support

Do you have an iPhone - or just an iPad?

An iPad, whether a Cellular model or not, is not capable of directly accessing Cellular Voice or SMS/MMS Messaging features. An iPad with either WiFi or Cellular connectivity alone can only access IP-data services.

However, If paired with an iPhone, the capabilities of iPad significantly broaden to include access to Cellular Voice and Messaging services of the associated iPhone - relayed to the iPad over WiFi using Apple’s continuity features.

More information about Continuity and the relevant Cellular services can be found here:

Continuity

Use Continuity to connect your Mac, iPhone, iPad, iPod touch and Apple Watch – Apple Support

SMS/MMS Messaging

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

WiFi Calling

Make a call with Wi-Fi Calling – Apple Support

If you have an iPhone - and both iPad and iPhone are signed-in to iCloud with the same AppleID, to send SMS/MMS messages from your iPad you must explicitly enable Text Message Forwarding for your [new] 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