Update Web Query Without deleting old data, just update new ones.

Hi, welcome to the forum
see attached file
Try this:

This sub calls itself every 10 minutes

Sub CopyList()
'set variables
    Dim wsD As Worksheet, wsH As Worksheet, rngD As Range, rngH As Range
    Set wsD = Sheets("Download"): Set wsH = Sheets("DownloadHistory")
'ranges to copy and paste
    Set rngD = wsD.Range("A1").CurrentRegion.Offset(2)
    Set rngD = rngD.Resize(rngD.Rows.Count - 2)
    Set rngH = wsH.Range("A" & Cells.Rows.Count).End(xlUp).Offset(1)
'copy and paste the data
    rngD.Copy rngH
'remove duplicates
    Set rngH = rngH.CurrentRegion
    rngH.RemoveDuplicates Columns:=Array(1, 2, 3, 4), Header:=xlYes
'repeat after 10 minutes
    Application.OnTime Now + TimeValue("00:10:00"), "CopyList"
End Sub

Do you want the sub to run automatically when the file is opened? Add this to the ThisWorkbook module

Private Sub Workbook_Open()
    Call CopyList
End Sub