I am assuming, you want the bursting stars over a static image that will remain visible throughout the animation. Do you already know how to build a gif?
Basics...assuming you do...otherwise you might want to skip down to reading material first.
Open the gif in Elements.
Drag your jpg image into the gif.
Place the image at the bottom of the layers stack.
Resize the jpg with free transform as it will be huge.
If the gif layer's do not have transparency around the bursting starts, remove the solid color on each layer.
Make a copy of the static jpg background for each gif layer.
Merge each gif layer with one of the static background copies.
Run layered file through Save for Web to make it animate and save in gif format. (Use the play button to view it.)
Optional: You can duplicate a layer (1 or more times) to create a delay or duplicate them all to slow down the entire effect. (Duplicating layers is the only way you can change timing in Photoshop Elements.)
The link below shows the dialogs and what to push in Save for Web:
Detailed write up but no images unlike the link above.
video tutorial on making an animated gif...however, I'd recommend reading the two links I've listed above first.
Other videos on the subject: (Note: Do not watch any using Photoshop as it's done different.)
Edit: If you go the other way...inserting gif into jpg, I'm not sure how well it'll hold up as Gifs are optimized to be really small. To make the drag and drop easy, link all of those animation layers; then grab the move tool and drag them into the jpg. While linked, you'll most likely want to resize the gif layers. They might not look so hot though if you resize them a lot. Do the rest like I said...make layers transparent and merge copies of the background with each frame, etc. Unlink those layers if any are linked before running the layers through Save For Web.