Navigate to the Vendors tab (or Clients, or Products) and click "Show Archived" to the right of the search bar near the top of the page.
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After the page refreshes, it should display ALL vendors (or clients, or products), including archived ones. You should see an icon that looks like this next to any archived ones:

Click on that to reactivate the vendor (or client, or product) and it will be available to use again.