King, for example, that is climbing Alpine height (5)
I believe the answer is:
eiger
'alpine height' is the definition.
The definition suggests a singular noun which matches the answer.
'king for example that is climbing' is the wordplay.
'king' becomes 'R' (abbreviation for rex, king in Latin).
'for example' becomes 'e.g.' (short for 'exempli gratia', 'for example' in Latin).
'that is' becomes 'ie' (abbreviation for id est, 'that is' in Latin).
'climbing' says the letters should be written in reverse (in a down clue, letters climb up).
'r'+'eg'+'ie'='regie'
'regie' reversed gives 'EIGER'.
Can you help me to learn more?
(Other definitions for eiger that I've seen before include "Swiss mountain with a notorious north face" , "North wall mountain" , "Mountains in Bernese Alps" , "Alpine mountain" , "Famous Swiss mountain" .)