Crossword Genius

Nouveau riche member of a mountaineering club? (6,7)

Ross

I believe the answer is:

social climber

I'm a little stuck... Click here to teach me more about this clue!

'nouveau riche' is the definition.
(thesaurus)

'member of a mountaineering club?' is the wordplay.
I cannot really see how this works, but
'member' could be 'limb' (member can mean a limb) and 'limb' is present in the answer.
'of' could be 'o' and 'o' is found in the answer.
'a' is found in the answer.
This explanation may well be incorrect...

Can you help me to learn more?

(Other definitions for social climber that I've seen before include "Upstart" , "One seeking higher status" , "Someone wanting higher status" , "One aiming for higher status" , "Parvenu" .)

I've seen this clue in the Sydney Morning Herald.
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