It's easy to do a picture-in-picture, if you don't mind the clock having a square background around it.
But if you want the clock to be round, you'll need to create the clock video segment in a program like After Effects from which you can output a transparent video.
Either way, you just put the clock clip on a video track above your main video track on your timeline and then resize it to the lower corner of your video frame.
Video is not computer, so I don't **think** you can do what you want
You could, however, create a frame at a time video of a clock... such as a series of JPG files with each JPG showing a different view of the clock face... and then use Picture in Picture (PiP) to put that video in a corner of your main video
Or, instead of frame by frame... put a camera on a tripod and film a clock, then use PiP to put that video in a corner
You might be able to use the trial version of NewBlueFX Video Essentials 4 without getting a watermark during the trial version. The package includes a Time Clock effect with various properties you can set. The effects are all digital, no hands on a round clock. http://www.newbluefx.com
Perhaps you could shoot a real clock on a green background and key it in as a chroma key? See help and other articles on how to do this.
Excellent! While I know of NewBlue FX, I had never looked at all of the features of their "Essentials." Much nicer way to do it, that what I was about to suggest - creating a Comp in After Effects with the TimeCode (not really a clock, per se), and then Importing that into PrE, and speed it up, as would be necessary. Your suggestion will be MUCH better, easier, and should give the OP exactly what they need. [Now I have to imprint your suggestion into my mind for later! ]