Ultimate challenge the day before a holiday (7)
I believe the answer is:
everest
'ultimate challenge' is the definition.
(tallest mountain in the world)
'day before a holiday' is the wordplay.
'day before' becomes 'eve' (the eve of something is the night before).
'a holiday' becomes 'rest' (rest can mean a holiday or break).
'eve'+'rest'='EVEREST'
'the' is the link.
(Other definitions for everest that I've seen before include "The highest mountain of all (7)" , "A high spot" , "The world's highest mountain" , "Mount, climbed 1953" , "Great achievement" .)