In principle, the rightsholders' permission is required if you want to include parts of an existing video or films in your video. You can contact the producer for this. The name of the producer can be found in the credits.
If a protected work appears very briefly by chance and in a subordinate way, permission doesn't need to be requested. Examples of this are buildings, posters or cars. You can also include extracts of images, long footage or works of art in educational or scientific recordings based on the right to quote. See copyright exceptions for more information.
Asking for permission to include parts of a film is often problematic. It often happens that the film producer is unknown, can't be found or doesn't respond to the request for use. In practice, the desired extract is sometimes used anyway. If you do that too, do realise that if the rightful rightsholder comes forward afterwards, an arrangement will still need to be made and in many cases compensation will have to be paid. In extreme cases, the extract may need to be removed.