Q: Contacts not syncing to Icloud

The following may have something that will help: Get help using iCloud Contacts, Calendars, or Reminders - Apple Support

Not sure what you would mean by "import from my sim card to the iCloud." There isn't any way to import from a sim card directly to iCloud.

The iPhone doesn't store contacts or other data on a sim card. The one and only thing it will do is if you have a sim card that has contacts on it that were placed on it from a previous phone (other than an Apple iPhone), it can import those from the card to the iPhone. See Import contacts from your SIM card to your iPhone - Apple Support

I'm not sure what it is that you are trying to do or the full path that you took to get to that screen. The one thing that I can say for certain is that there is no iPhone that writes contacts to a SIM. The iPhone does have the ability to import Contacts from a sim if the sim originated from a previous non-Apple iPhone.

Sorry but other than all of the steps in Get help using iCloud Contacts, Calendars, or Reminders - Apple Support I don't have any other suggestions. The most frequent issue that I have seen reported here has to do with the contacts being in some other account as discussed in the iPhone, iPad, or iPod Touch section of that link.

My iPhone 5s will not receive updates from iCloud AUTOMATICALLY.

If I make a change to a contact on my iMac it flows immediately to iCloud. I can see it on iCloud and on my iPad, but the iPhone will not sync it UNLESS I DO A MANUAL SYNC by tapping Contacts -> Groups, and doing the 'pull down' with my finger which will start the spinning gear.

What is causing the iPhone to not get the the new data from iCloud automatically?

Have you tried signing out of iCloud and then sign back in?

Yes, I tried signing out and back in. Did not work. What is interesting is that the Calendar and Notes get updated on the iPhone from iCloud, but not contacts. It must be something with the Contacts app that is blocking updates... unless I do it manually.