Hosting the trailer on your site without permission is definitely not allowed, but you are probably allowed to embed a YouTube player with the video. In that situation you'd only need to check YouTube's terms of use, not the original copyright holder (disclaimer: I'm not a lawyer and the legal situation may also depend on the jurisdiction).

See also https://support.google.com/youtube/thread/21846505

Hello.It's the violation of copyright to post Movie Trailer Videos on the websites of other people.Your contents should be free from the copyright,else you will be in the bars,if,the Manager of the website complains against you.This is followed by 'Youtube'.Your channel will be blocked,if you post any Video,that has the copyright material.It should not be done.Thanks.