First lady may relax on great peak (7)
I believe the answer is:
everest
'great peak' is the definition.
'everest' can be an answer for 'peak' (Everest is an example). I am unsure of the 'great' bit.
'first lady may relax on' is the wordplay.
'first lady may' becomes 'eve' (I am not sure about this - if you are sure you should give a lot more credence to this answer).
'relax' becomes 'rest' (to relax is to have a rest).
'on' is a charade indicator (letters next to each other).
'eve'+'rest'='EVEREST'
Can you help me to learn more?
(Other definitions for everest that I've seen before include "Huge achievement - highest climb" , "The highest mountain of all (7)" , "Himalayan peak" , "Great achievement" , "Mountain on the Nepal-Tibet border" .)