#1 climb up v. go upward with gradual or continuous progress; "Did you ever climb up the hill behind your house?". wn
#2 climb up v. appear to be moving upward, as by means of tendrils; "the vine climbed up the side of the house". wn
#3 climb up v. rise in rank or status; "Her new novel jumped high on the bestseller list". wn
vizzz