If you do something promptly, you do it immediately.
Sister Francesca entered the chapel, took her seat, and promptly fell asleep.
弗朗西丝卡修女走进小教堂,就了座,很快就睡着了。
If you do something promptly at a particular time, you do it at exactly that time.
Promptly at a quarter past seven, we left the hotel.
我们在7:15准点离开了旅馆。