Synonyms for Climber (same or very similar meaning)
WordNet sense 1 (someone seeking social prominence by obsequious behavior):
social climberWordNet sense 2 (someone who ascends on foot):
mounterWordNet sense 3 (an iron spike attached to the shoe to prevent slipping on ice when walking or climbing):
crampon, crampoon, climbing ironFrom the ODE community, based on WordNetadd/edit