Wiktionary
vb. 1 (context intransitive English) to make a gradual ascent or increase 2 (context transitive English) to gradually ascend something
WordNet
Usage examples of "climb up".
And the true realism were that of the poets, to climb up after him like a squirrel, and catch some glimpse of the heaven for which he lives.
Then a short climb up a cleft and they stood together on top of the ridge.
The exertion of climbing the fixed ropes at high speed was just enough to keep them warm on the climb up.
Sometimes the smell of the morning bread from the ovens took him to the kitchens, and sometimes he would climb up to the roof garden or wander all alone down Traitor's Walk.
Smoke and cinders swirled through the air, and the foe broke before their charge, throwing themselves back into the water, knocking over other men as they fought to climb up.