Mount Cook’s top reached by member (5)
I believe the answer is:
climb
'mount cook's top' is the definition.
'climb' can be an answer for 'mount' (synonyms). I am not certain of the 'cook's top' bit.
'reached by member' is the wordplay.
'reached by' becomes 'c' (I can't justify this - if you can you should give a lot more credence to this answer).
'member' becomes 'limb' (member can mean a limb).
'c'+'limb'='CLIMB'
Can you help me to learn more?
(Other definitions for climb that I've seen before include "Slope upwards" , "Go upwards" , "What mountaineer does" , "Go up - scale" , "Deadened" .)