To do something promptly is to do it right away or in a timely fashion, avoiding any delays.
When you receive an invitation, you might immediately check your calendar and promptly reply. Doing things promptly is the opposite of procrastinating or putting things off. Showing up promptly for meetings, dates, and other plans is courteous and polite. When the President responds promptly to a crisis, it's considered good leadership. If you delay too much, you lost the chance to do something promptly — this is a word for things that happen fast.