Let me see if I can pick up where @rolandh was going, and he can follow up if I miss anything.
Since the SIM card in your new phone is GSM, yes, it can be moved to the Moto G4 Play if you should need to re-activate that phone as an emergency back-up.
You may very well want to keep the old SIM card in the old phone for just one reason - that Moto G4 Play requires the “Micro” SIM card size. The new phone has a smaller “Nano” size SIM card. To use the “Nano” sim in the Moto G4 Play, you would need an adapter - a little plastic “frame” that the Nano SIM snaps into to bring it to the “Micro” size. That frame was included in the credit-card size SIM card holder that your new SIM card snapped out of, but you may have already thrown that away, and if not, it can be hard to keep up with. The SIM card in your Moto G4 Play is currently snapped into one of those adapters. So if you ever need to put the G4 Play back in action, you could pull out its SIM card, snap the adapter off if its old SIM card, put the adapter on the new phone’s Nano SIM, and insert the new phone’s SIM card, now adapted to Micro size, into the G4 Play.
If you’re better at keeping up with things than I am, you may have a better solution for keeping that adapter handy, but it just seems to me that having it in the phone itself would be an easy solution.