When something happens apace, it happens quickly. You could say that despite the rain, your house painting project is still continuing apace.
You're most likely to see the adverb apace describing some kind of work, and it's usually paired up with the verb continue. A harried theater director might insist that progress on the new play continues apace, or you might notice that your next door neighbor's chicken coop construction is continuing apace, progressing rapidly. The literal meaning of the 14th century phrase a pace was "at a pace," or "at a good pace."