pull down over
pull (something) down over (someone or something)
To drag or draw something over the top of someone or something from a higher position so that it covers them or it. I pulled the hat down over my face in embarrassment. The doctor tore the exam table paper off after her patient left and pulled a fresh sheet down over it.
pull something down over someone or something
to draw something down over someone or something. Lucy's mother pulled the dress down over Lucy and buttoned it up in back. Sarah pulled the cover down over the birdcage and turned out the lights.