The most common and most likely answer to this crossword clue is the 8 letter word ALPINIST
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More clues leading to the result ALPINIST
Buddy explains!

The straight part
We know that "climber" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case climber = alpinist.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.
What does ALPINIST mean?
ALPINIST noun- A skier who specializes in alpine skiing (the disciplines of super-G, giant slalom, slalom, downhill)
- (sometimes capitalized) A mountain climber, especially in the European Alps or in ranges of similar ruggedness and elevation.
- (sometimes capitalized) A downhill skier who practises the sport on high mountains.
- Of or pertaining to alpinism.
- Pertaining to alpine skiing or downhill skiing.