Are your Part Numbers in a table and the combo based on a query of that table?

If so, open a form on the PartNumbers table and add the record. When you
close the form you will return to the combo and the new item should appear in
your list.

Private Sub myCombo_NotInList(NewData As String, Response As Integer)
If MsgBox("This part number is not in the drop down menu, would you like to
add the new part number?",vbQuestion,"Add a new part number?") = vbYes Then
DoCmd.OpenForm "myForm", , , ,acFormAdd ,acDialog
End If
Me.myCombo.Requery
End Sub

If your table only has one column (doubtful for part numbers) you could just
use an INSERT query to insert the value entered, from NewData.

Private Sub myCombo_NotInList(NewData As String, Response As Integer)
Dim strSQL As String

If MsgBox("This part number is not in the drop down menu, would you like to
add the new part number?",vbQuestion,"Add a new part number?") = vbYes Then
strSQL = "INSERT INTO tblPartNumbers VALUES (NewData);"
CurrentDb.Execute strSQL, dbFailOnError
End If
Me.myCombo.Requery
End Sub

The second example could/would mean that new part numbers are added to a
table without any description or other information that I would have thought
any part number would need.

Anyway, hope that helps!

Steve