move up

to increase in value, number, or amount:
Share prices move up and down depending on market conditions.

to get a more important job in a company or organization:
move up to sth
He gave his first interview since moving up to the role of chairman.

move up the ranks/ladder
Gaining further qualifications can help you move up the career ladder.
(Cambridge ビジネス英語辞典 からの move up の定義 © Cambridge University Press)

- Cambridge Dictionary