A lot of web pages offer instructions for creating shine effects in The GIMP, but here’s one easy procedure I didn’t find:

1. Create whatever image you want to impose the shine on
2. Create a new layer above the image and fill it with the shine color (usually white)
3. Set the new layer’s opacity to 50-60%
4. Add a layer mask, initialized to black (fully transparent) and select the mask for editing
5. Select the region you want to include the shine
6. Feather the selection by, say, 20-30px (newer versions of GIMP let you do this from the selection tool itself, by checking the “Feather Edges” box before you start selecting)
7. Fill the selection with a gradient from black to white

And you get something that looks like this:

(and here’s the XCF source image)

Bonus: the GIMP’s window icon for this image looks like the Death Star ;-)