There are several synonyms for the phrase "moving up". One common synonym is "advancing", which refers to making progress or moving forward in a particular field or endeavor. Another synonym is "ascending", which implies a gradual upward movement. One can also use the phrase "climbing the ladder", which refers to progressing through different levels of a hierarchy or job position. "Elevating" is another synonym, which suggests a rise in status or importance. Other synonyms include "proceeding upward", "promoting", and "scaling new heights". Overall, these synonyms suggest progress, growth, and achievement.