I did carrier update on my phone yesterday and since then I keep getting "no SIM card installed" or no service notices. rebooting fixes the problem, but then it happens again a little while later. Live in Newmarket. Have an iPhone6 with iOS 10.3.2 on a monthly plan.
Try taking the Sim card out and put it back in again and then restart it. It seems unlikely given it started when you got the update but it might need a new Sim if it keeps up. Generally how long does it take before it happens again after a restart?