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.

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.