The crossword solution for the term 'container that surrounds 'vanity case'' is VASE, which is a four-letter word. A VASE is a container typically used to hold flowers or other decorative items. It is usually made of glass, ceramic, or metal and can come in a variety of shapes and sizes. In this context, it is being used to surround a vanity case, which is a small box or case used to store personal items such as makeup, jewelry, and other accessories.