Can I use a movie trailer for an artist's show?

Probably not, without permission of the owner of the copyright in the movie trailer. Copyright law protects works of authorship that are fixed in a tangible medium of expression from being copied and publicly displayed without the owner's permission. A movie trailer would certainly be protected under copyright law. Additionally, the people who appear in the movie trailer have a "right to privacy" (or publicity right) that prevents the use of their images by someone else for commercial purposes.