Definitions of climber:

• noun:   someone who climbs as a sport; especially someone who climbs mountains

  Example: "The lead climber looked strong still but his partner often slumped in his ropes"

• noun:   a vine or climbing plant that readily grows up a support or over other plants
• noun:   someone who ascends on foot
• noun:   someone seeking social prominence by obsequious behavior
• noun:   an iron spike attached to the shoe to prevent slipping on ice when walking or climbing