How does one duplicate a fancy design on a frame that is missing?

Shirley: you can use silicone putty... like in this video

https://www.youtube.com/watch?v=HHTcm1VJpSA

You can use a glue gun. Put the hot glue over another piece identical to the one that is missing. When it has cooled, peel it off and use that as a mold. Make a new piece with clay, or plaster of Paris or paper clay. Cut to fit the missing area and repaint of finish.

Can you take a picture and share?

See if this helps

https://www.youtube.com/watch?v=P2D6R0Lw22k

Here's how to make a mold and repair

https://www.hometalk.com/diy/repair/furniture/repair-that-missing-trim-37624897

Here's another good tutorial for you: https://www.youtube.com/watch?v=_mZXvijwj8E

Use some silicone sealer to make a mold. Once dry remove and filler the mold with wood filler.

Hello. I usually carve one out of clay or wood filler and repaint

Hi Shirley, we've used our home made silicone mold to recreate missing bits on a frame. You can get the tutorial to make your own mold here - https://acraftymix.com/blog/two-ingredient-mold/