Are you having difficulties with all received messages reaching your new iPad - or just SMS/MMS messages that are relayed from an associated iPhone? Something else?
Assuming that all devices are signed-in to iCloud with the same AppleID - and that you have an iPhone - to send SMS/MMS messages (green bubbles) from your iPad you must explicitly enable Text Message Forwarding for your old and 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 iPad’s and your iPhone:
Settings > [Your Name / AppleID] > Messages - set to ON