doors open up
Opportunities arise. I'm sure that when you're a CEO's daughter, doors open up to you regardless of what's on your resume. Casey is the head of our department, so I really think you'll see doors open up if you impress her.
doors open up
(to someone) opportunities become available to someone. After Ann made a few inquiries, doors began to open up to me. An agent helps. After I got one, all sorts of doors opened up.