New phone will not work with old sim card.

I recently bought a new Iphone 6s. I tried transferring my sim card from my iphone 5(worked completely fine) to this new, unlocked iphone 6s that I bought. When I did, the service worked extremely inconsistently, and more than not I was unable to use any phone services. There would be times where I could call from this new phone, but usually it either said no service or it showed my company in the corner of the iphone and would still not work. I have tried contacting chatr multiple times to fix it, but nothing they done has helped. Also, I bought a new sim card and it still does not work consistently in the new phone. What should I do?