1. To have a higher rank or position than someone in a business, government, or military hierarchy. Well, I technically rank above Sarah, but we operate more like equals in the office. He ranks above you, so you'd better do what he says.

2. To be considered more valuable, significant, or important than another person, thing, or group of people or things. I believe preserving the wellbeing of our fellow citizens ranks above trying to maximize the profits of corporations. Although he is largely written off by music aficionados, he still ranks above nearly every other singer on the billboards every time he releases a new album.

3. To consider someone or something to be more valuable, significant, or important than another person, thing, or group of people or things. In this usage, a noun or pronoun is used between "rank" and "above." I wouldn't rank it above her other work, but it's still a very well-written piece of literature. We rank Sarah above any other lawyers in the city, so we have full confidence in her ability to handle this case on her own.