We will assist you in the order in which you were received. We ask for your patience.
「順番にご案内/対応している為返信にお時間を頂いております」という表現を英訳すると「We will assist you in the order in which you were received. We ask for your patience.」という表現になります。とても丁寧なニュアンスがあります。この場合、「順番に」という言葉は「the order in which you were received」になります。