Mount Everest's two lowest sections require no name (5)
I believe the answer is:
steed
'mount everest's' is the definition.
'steed' can be an answer for 'mount' (I've seen this before). I am unsure of the 'everest's' bit.
'two lowest sections require no name' is the wordplay.
'two lowest sections' becomes 'st' (I am not sure about this - if you are sure you should believe this answer much more).
'require' becomes 'need' (synonyms).
'no' is a deletion indicator.
'name' becomes 'n' (common abbreviation e.g. on forms).
'need' with 'n' taken away is 'eed'.
'st'+'eed'='STEED'
Can you help me to learn more?
(Other definitions for steed that I've seen before include "(Poetic) horse" , "Literary term for horse" , "ride" , "A mount (poet.)" , "Stallion" .)