My new iPad will not send messages to certain recipients.

Sending Messages from Apple to Apple Devices uses wi-fi.

Sending Messages back and forth with Android users requires Cellular data. (Provider charges may apply)

For IPad models with Cellular: You may want to check your cellular settings for Messages:

How to: View or change cellular data settings on iPad (Wi-Fi + Cellular models) - Apple Support

Thank you for your reply. We do not know what recommendations you actually have tried, or what happens when you try to send, or whether you are getting an error message that would point to the cause of the situation.

Eg: If you haven't done so already: you may want to check the new iPad's iPadOS version is up-to-date with the newest version. (If needed: You can check to see if there is an update ready to install in Settings > General > Software Updates. Eg: About iPadOS 18 Updates - Apple Support says: iPadOS 18.2 is the latest.

(NB: It is always wise to back up your iPad data before updating)

If you have un-necessary third-party (non-Apple) apps like ad-blockers, virus checkers, cleaners, and the like, even VPN, installed ... try turning them off (or uninstall them) to see if they are are causing issues. Any third-party apps considered necessary may need to be up-to-date with the newest versions in order to remain compatible.