That's possible through Spotify Canvas. A Canvas is a video up to 8 seconds long that is displayed in a continuous loop in a vertical format on the screen while your track is playing.

It will be displayed instead of your album/track art when someone listens to your track. You can add a canvas to any of your songs, including future releases.

Required for this is access to your Spotify for Artists.

Here's how: Click Release > Edit Canvas > Edit > Create new Canvas > Choose Artwork > Choose Video > Trim between 3 and 8 seconds > agree and publish.

You can also find Spotify's instructions here under "How to add a Canvas".