Add video banner on our WP page

We have a Wordpress page with KLEO theme installed. We are now wanting to add a different entrance to our webpage by adding a video banner full width and clean minimalistic links on the top over the video image. We do not want to make any changes of theme or other big changes to our page. Just add this video feature together with a mobile menu option also.

Also the video should be self hosted and start immediately when a user is entering the page. Here are some samples of how it could look.
https://www.isabellalowengrip.se
http://themetrademark.com/demo/naila/?page_id=109
https://drivestudios.dk (our favorite)

We will of course provide the video itself.