To occupy a lot of space (physically), or figuratively to dominate the scene/attract attention.
彼の大きな展示作品が会場で場を取っていた。
His large exhibit was taking up space at the venue.
彼女はいつも話し方で場を取るので、会議の流れが変わってしまう。
She always takes over the room with the way she speaks, so it changes the course of the meetings.