move up to
1. Literally, to move someone or something to a higher physical location. In this usage, a noun or pronoun is used between "move" and "up." Would you move the pans up to the next shelf so I can use this one for plates? I moved up the painting a little bit from where you had it. I just think it fits the space of the wall a bit better now.
2. To advance or elevate one's position. I was only in the company for a few months before I started moving up. It's unsurprising how quickly Sarah has moved up in the company—her tenacity and determination are matched only by her intelligence and talent.
3. To advance or elevate someone else's position. In this usage, a noun or pronoun is used between "move" and "up." I hear they only moved him up because he has some dirt on the CEO.
4. To elevate or improve one's social, political, and/or financial position in life; to become more successful than one was before. You're only going to truly move up in the world if you make a point of rubbing elbows with those of a higher social standing. The Robinsons really moved up in life after they won the lottery.
move up to
advance; to go higher. Isn't it about time that I move up? I've been an office clerk for over a year. I had hoped that I would move up faster than this.