Go to the DOT with your old ID and just tell them the new adress and they will give you a new License you will pay for without the yellow star. If you plan to fly though you will need the license with the star on your ID so if you dont want to pay another license fee just go with your ssi card and birth certificate. I went to update my adress and they wouldnt give me the license with the star even though I had my old License with me, stupidist rule and made absolutely no sense.
Here's a link that will help you determine what you need - https://iowadot.gov/mvd/realid/
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