Beginner abandons most demanding challenge (7)
I believe the answer is:
everest
'challenge' is the definition.
(Mount Everest, a challenge for mountaineers)
'beginner abandons most demanding' is the wordplay.
'beginner abandons' means to remove the first letter.
'most demanding' becomes 'severest' (severe can mean hard or demanding).
'severest' with its initial letter removed is 'EVEREST'.
(Other definitions for everest that I've seen before include "The highest mountain of all (7)" , "High peak" , "Highest Himalayan mountain" , "A mountain to climb" , "Highest peak" .)