I would give the plastic a good wiping-down with alcohol and let it air-dry. A good spray adhesive should do the job (3M upholstery adhesive comes to mind….) just don't soak it on. Spray a light coating to both the panel AND the backside of the material. Allow it to set up for a minute, and CAREFULLY apply using a soft squeegee to get the air & wrinkles out.

Go slow and practice with scrap to get a feel for how the material will stretch and apply.