Ultimate challenge: getting First Lady to have a siesta? (7)
I believe the answer is:
everest
'ultimate challenge' is the definition.
(tallest mountain in the world)
'first lady to have a siesta?' is the wordplay.
'first lady' becomes 'eve' (first woman in the Bible).
'to have' means one lot of letters go next to another.
'a siesta?' becomes 'rest' (I've seen this in another clue).
'eve'+'rest'='EVEREST'
'getting' is the link.
(Other definitions for everest that I've seen before include "Where Hillary was" , "The world's highest mountain" , "Mount, climbed 1953" , "One conquered in 1953" , "The highest mountain of all (7)" .)