Excel Sort function on the active range

There's also a new Dynamic Array function SORT which you could use.

Keep the existing sheet, with the data established as an official Excel Table.
Then use SORT on a second sheet to produce a sorted version of that Table
Do all your additional rows in the original (unsorted) table. They will automatically be added to and resorted in the second version. It's basically separating the raw data (Input) from the Output.

Here are two resources to learn more about SORT and some other of the Dynamic Array functions.

https://www.youtube.com/watch?v=9I9DtFOVPIg

https://exceljet.net/excel-functions/excel-sort-function

FrankWitsel 

If you want to sort the data in place, you could use VBA code to sort the table when the workbook is opened, and if desired also when you switch to the relevant sheet from another sheet in the workbook.

(Sorting automatically as data are being added/edited is not a good idea, it would look very confusing.)

To do so:

1) Press Alt+F11 to activate the Visual Basic Editor.

Select Insert > Module.

Copy the following code into the module:

Sub SortData()
    With Worksheets("Sheet1")
        .Range("A1").CurrentRegion.Sort Key1:=.Range("J1"), Header:=xlYes
    End With
End Sub

Change the name of the sheet to the one containing the table, and change A1 and J1 if the table does not start in A1.

2) Double-click ThisWorkbook under Microsoft Excel Objects in the Project Explorer pane on the left.

Copy the following code into the ThisWorkbook module:

Private Sub Workbook_Open()
    Call SortData
End Sub

This will sort the data when the workbook is opened.

3) Double-click the relevant worksheet in the Project Explorer.

Copy the following code into the worksheet module:

Private Sub Worksheet_Activate()
    Call SortData
End Sub

This will sort the data when you switch to the worksheet from another sheet in the same workbook.

4) Switch back to Excel.

Save the workbook as a macro-enabled workbook (.xlsm).

Make sure that you allow macros when you open the workbook.