Substitute a portion of a video with a still image?

As with most film clips, I have some footage with sound attached. I was wondering if there’s a way to substitute a portion of the video of part of the clip with a still image, say to superimpose that image over the existing video, without having to re-record the audio for that portion of the clip.

In other words, say I’m talking about something, and for a moment or so I want to continue talking about it in the clip but I want to replace existing video with, say, a still image of what I’m talking about for that portion of the audio.

Is there a way to do this? If not, I can just break into the video/audio to show the still for a moment, but I thought it would be better if I could continue the audio while temporarily showing the still that I’m talking about.