Move a row from one worksheet to another when a date is entered in the Date Claimed column

Well, the first thing you should know about VB is that is pretty spreadsheet specific, so we'll be able to little without an attachment provided.
I'd recommend scrubbing your data and providing at least a rough outline.

That said, you'll need to utilize a worksheet change event to continuously run through sheet1 every time something changes. When it does, it'll copy the relevant data. We toss in a filter to re-sort page 1 to fill in the gaps after the cut & paste.

This code goes directly on the worksheet instead of in a module.

Private Sub Worksheet_Change(ByVal Target As Range)

If Target.Column = 9 And Target.Row > 1 Then
    Target.EntireRow.Cut Sheets("Found").Range("A" & Rows.Count).End(xlUp).Offset(1)
        With Worksheets("Lost").Sort
            .SetRange Range("A2:I99")
            .Orientation = xlTopToBottom
            .Apply
        End With
End If

End Sub