I had the same problem , except no incoming calls were getting through, all sending directly to Voicemail. After talking to my carrier for over half an hour and Apple Chat Line for about as long, it still was not receiving calls. Everything else worked, iMessage, FaceTime, outgoing calls, even voicemail once I got it set up. At the top left of the phone I had plenty of bars and the name of the carrier next to which was LTE.
I got it working myself! I was going through EVERY THING in my settings directory for the hundredth time, just about to give up and see if I could send the phone back. When I found this that got it working: in SETTINGS go to CELLULAR/CELLULAR DATA OPTIONS/VOICE & DATA. I switched it from LTE to 3G. Now it receives calls, no problem. Apparently I don’t have LTE service. Maybe you don’t either.