You can change the skin of the existing gallery.
Please follow the below steps:
1. Go to "My galleries"
2. Click "Edit Gallery"
3. Click "Change skin"
4. Choose the media type and the skin design.
5. Choosing skin will open a preview of the chosen skin. Click "Use this skin" if you like it.
Choose another skin if you don't like it by clicking 'Back to skins'
6. All changes are automatically saved and preview updates automatically at each change.
Note: There is no need to re - embed your gallery again
Just refresh your website and you will see that the gallery skin is changed.