The most common and most likely answer to this crossword clue is the 10 letter word DERAILLEUR
I've seen this crossword clue in The Times
D
E
R
A
I
L
L
E
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R
Buddy explains!

The straight part
We know that "that’s applied to cycles" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case that’s applied to cycles = derailleur.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 DERAILLEUR mean?
DERAILLEUR noun- The mechanism on a bicycle used to move the chain from one sprocket (gear) to another.
- The entire gearset on a bicycle with such a mechanism.