Period of limitation whether mandatory

The High Court while quashing and setting aside the lower court order granted liberty to the appellant to file fresh suit, with the necessary notice of motion, within four weeks from the date of the order of the designated officer (BMC). Now, is it mandatory for the appellant to prefer and file suit after the period as granted by the HC is over? Is it 'ok' for the lower court to entertain the suit after the period granted by the HC as above is over?