The most common and most likely answer to this crossword clue is the 10 letter word ESCALATION
I've seen this crossword clue in The Times
E
S
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A
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Buddy explains!
The straight part
We know that "Rapid rise" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case rapid rise = escalation.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 ESCALATION mean?
ESCALATION noun- An increase or rise, especially one to counteract a perceived discrepancy
- A deliberate or premeditated increase in the violence or geographic scope of a conflict
- (customer support) The reassignment of a difficult customer problem to someone whose job is dedicated to handling such cases.