Mountain most demanding in leader’s absence (7)
I believe the answer is:
everest
'mountain' is the definition.
(Mount Everest)
'most demanding in leader's absence' is the wordplay.
'most demanding' becomes 'severest' (severe can mean hard or demanding).
'in leader's absence' means to remove the first letter.
'severest' with its initial letter taken off is 'EVEREST'.
(Other definitions for everest that I've seen before include "A mountain to climb" , "Himalayan mount" , "Himalayan peak" , "The highest mountain of all (7)" , "Mount, climbed 1953" .)