Cryptic crossword clue
Getting more extreme, if CIA’s muddled in aim 15

The most common and most likely answer to this crossword clue is the 15 letter word INTENSIFICATION

I've seen this crossword clue in The Sunday Telegraph
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Buddy explains!

The straight part
We know that "Getting more extreme" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case getting more extreme = intensification.
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 INTENSIFICATION mean?

INTENSIFICATION noun
  1. The act or process of intensifying, or of making more intense.

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