Mountain peak I start to climb, taking step up (3,3)
I believe the answer is:
ice cap
'mountain peak' is the definition.
(an ice cap may cover the top of a mountain)
'i start to climb taking step up' is the wordplay.
'start to' says to take the initial letters.
'taking' says to put letters next to each other.
'step' becomes 'pace' (synonyms).
'up' shows that the letters should be reversed in order (in down clue: letters go upwards).
The first letter of 'climb' is 'c'.
'pace' back-to-front is 'ecap'.
'i'+'c'+'ecap'='ICE-CAP'
(Other definitions for ice cap that I've seen before include "Permanently frozen mountain-top mass" , "Frozen polar region" , "polar area" , "Permanent covering of frozen water" , "Polar feature" .)