I’ve always done the same and did so this time with the new iPad Pro. First I had both devices shut down. I had not started up the new one yet so no activation had occurred. Then I removed the SIM card from my old iPad while it was shut down. I placed it into the new one. Then I restarted the old one, I wanted to use that quick set up mechanism, got the No Sim message and tapped on ok. Then I started up the new one for the first time. The quick set up process was offered and everything set up properly including cell service with no issues.
If your cell service was not activated you could try shutting the device down and removing the sim and making sure it is properly placed in the sim tray, I had to fiddle with mine a bit before it was seated properly in the tray, clumsy fingers. Then push it back in and restart. If that still doesn’t work you might want to visit a Verizon store and have them help you out. But I’ve done this with 3 different iPads using the same SIM card from several years ago. I haven’t had any issues. I am with att but that shouldn’t make any difference.