'move up' definitions:

Definition of 'move up'

From: WordNet
verb
Move to a better position in life or to a better job; "She ascended from a life of poverty to one of great [syn: ascend, move up, rise]
verb
Move upward; "The fog lifted"; "The smoke arose from the forest fire"; "The mist uprose from the meadows" [syn: rise, lift, arise, move up, go up, come up, uprise] [ant: come down, descend, fall, go down]