Give this a try. Instead of Worksheet Change, you need to use Worksheet SelectionChange. Also, added a line to remove all previous values and a line to find LastRow of table.
Code:
Private Sub Worksheet_SelectionChange(ByVal Target As Range)
Dim rngActiveCell As Range
Dim lngLastRow As Long
Dim lngTblColNum As Long
Dim LastRowTable As Long
If Target.Column < 4 Then
Set rngActiveCell = ActiveCell
lngLastRow = ActiveCell.Row
If Not Intersect(ActiveCell, [Table1]) Is Nothing Then
LastRowTable = ActiveSheet.ListObjects("Table1").DataBodyRange.Rows.Count + 2
Range("V3:V" & LastRowTable).Value = ""
Range("V" & lngLastRow).Value = "Active"
End If
End If
End Sub