First lady taking break on mountain (7)
I believe the answer is:
everest
'mountain' is the definition.
(Mount Everest)
'first lady taking break' is the wordplay.
'first lady' becomes 'eve' (Biblical first woman).
'taking' is a charade indicator (letters next to each other).
'break' becomes 'rest' (a rest is taking a break).
'eve'+'rest'='EVEREST'
'on' acts as a link.
(Other definitions for everest that I've seen before include "Himalyan peak" , "Huge achievement - highest climb" , "Where Hillary was" , "Himalayan peak" , "The world's highest mountain" .)