The most common and most likely answer to this crossword clue is the 7 letter word HILLARY
I've seen this crossword clue in Financial Times
H
I
L
L
A
R
Y
More clues leading to the result HILLARY
Buddy explains!

The straight part
We know that "Legendary climber/unable to break the glass 10" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case legendary climber/unable to break the glass 10 = hillary.The cryptic/wordplay part
In cryptic crossword there's often an wordplay/cryptic part as well.This part involves a more complex hint, such as an anagram, homophone, hidden word, etc.
Sadly, We don't have an explanation for this specific crossword clue yet.