Primary domain still shows search results from old website

Hi everyone!

I’m making a website for a client. He had a website with a domain that he wanted to keep using with the new website. So I made a website with a temporary domain while I was working on it. Once it was ready, I switched out the temporary domain that I was using with the one from his old website. Now, when I search up his brand, it still comes up with the old google search results, with old headers underneath. When I click on it, it takes me to the new website that I made. I used Yoast SEO to make new google search results, so I don’t understand why it’s still coming up with the old one?

I hope someone in here can help me fix this issue, as it’s been stressing me out for the past few days :0


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