Two options I think:
One option is to copy paste the video's URL into your instance's search box and search for it there. You'll have to have the "Allow users to do remote URI search" switched on.
Another option is to set your instance to allow searching on the global index, it will allow you to search for videos that aren't on instances you federate with. (Bear in mind the global index isn't moderated, so this probably isn't something you want your users to see.)
Official documentation is here, have a look at the section on Search which covers both these options: