The ability to send SMS texts (green texts) relies on setup that occurs on your iPhone, so that is where I would go to investigate this problem. Look in Settings > Messages > Text Message Forwarding in the iPhone. You should see the iPad listed in there; it may even have the slide switch enabled. If it is enabled, and still not working, try the time-honored technique of turning it off and then back on again, which I believe will involve a verification code sent to the iPad, and may invoke a sign-in to your Apple ID. If that still doesn't do it, I would try signing out of iCloud on all your devices, and then signing in again.