Old man climbing Everest's first to cross summit (4)
I believe the answer is:
apex
'summit' is the definition.
(I've seen this before)
'old man climbing everest's first to cross' is the wordplay.
'old man' becomes 'pa' (both can mean someone's father).
'climbing' says the letters should be written backwards (in a down clue, letters climb up).
'everest's first' becomes 'e' (1st letter of 'everest').
'to cross' becomes 'x' (X is cross-shaped).
'pa' backwards is 'ap'.
'ap'+'e'+'x'='APEX'
(Other definitions for apex that I've seen before include "Peak, vertex" , "Summit - pinnacle" , "Point or summit" , "The highest point or pointed end" , "reasonable fare" .)