Place your video on track 2. Add Generated Media Gradient to track 1. You can play with the control points of the generated media to get white on top fading to transparent in the middle and fading back to white again in the middle. Adjust the track level slider for overall opacity.

If you want something fancier than solid white, insert a new track between 1 and 2 and put a noise texture inbetween the gradient and the video. Add the Mask effect to track one and set the compositing mode to Multiply (Mask). You'll now be superimposing a noise texture onto your video and using the gradient to mask it to just the top and bottom. Maybe starting with one of the cloud textures would be good beginning point. Changing the parameters can help soften it.