[NumLock]

у TListView событие OnCompare. в справке также есть пример сортировки по колонке по которой кликнули мышкой:

This example shows how to use the OnColumnClick and OnCompare events of a list view to let users sort the columns in a report-style list view by clicking on the column headers. This requires a global variable to keep track of the column that was clicked:

var ColumnToSort: Integer;

The OnColumnClick event handler sets the global variable to indicate the column to sort and calls AlphaSort:

procedure TForm1.ListView1ColumnClick(Sender: TObject; Column: TListColumn);

begin
ColumnToSort := Column.Index;
(Sender as TCustomListView).AlphaSort;
end;


The OnCompare event handler causes the list view to sort on the selected column:

procedure TForm1.ListView1Compare(Sender: TObject; Item1, Item2: TListItem; Data: Integer; var Compare: Integer);
var
ix: Integer;
begin
if ColumnToSort = 0 then
Compare := CompareText(Item1.Caption,Item2.Caption)
else begin
ix := ColumnToSort - 1;
Compare := CompareText(Item1.SubItems[ix],Item2.SubItems[ix]);
end;

end;

Note: This OnCompare event handler uses the global CompareText function. An application may want to use AnsiCompareText, CompareStr, or AnsiCompareStr instead, depending on whether the comparison should be case-sensitive and whether the locale should be considered.