Most intelligent tips from climber leaving mountain (9)
I believe the answer is:
cleverest
'most intelligent' is the definition.
'tips from climber leaving mountain' is the wordplay.
'tips from' says to take the initial letters (I've seen 'tip from' mean this).
'mountain' becomes 'everest' (I've seen this before).
The initial letters of 'climber leaving' is 'cl'.
'cl'+'everest'='CLEVEREST'
(Other definitions for cleverest that I've seen before include "of superlative brilliance" , "most able" , "Brighter than others" , "Smartest" .)