When a reader searches for a book on Goodreads, there is one edition that always appears—the Primary (or Default) Edition. If you update your book's cover and you want the new cover to appear when readers search for your book, you must set the new cover edition as the Primary Edition.
The following directions came from the Goodreads site.
1) Navigate to the book's page. Be sure you have selected the edition you wish to become the default (primary) edition.
2) Click "edit details" below the book's description.
3) On the right side of the page, click "Set this book as the primary edition for this work". It's about midway down the page.
Only Goodreads Authors can set the default edition at this time.