move up phrasal verb ( see also ↑ move )
1 . to get a better job in a company, or change to a more advanced group, higher rank, or higher level:
To move up, you’ll need the right training.
Share prices moved up this month.
move up to
The kids learn fast, and can’t wait to move up to the junior team.
He was moving up the ladder (=getting higher and higher positions) , getting experience of command.
He’s moved up in the world (=got a better job or social position) in the last few years, and his new flat shows it.
2 . especially British English to change position in order to make more space for other people or things or be near someone else:
There’s room for one more if everyone moves up a bit.