The most common and most likely answer to this crossword clue is the 14 letter word LIFE-AND-DEATH
I've seen this crossword clue in Financial Times
L
I
F
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A
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D
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D
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More clues leading to the result LIFE-AND-DEATH
Buddy explains!

The straight part
We know that "critically important" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case critically important = life-and-death.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 LIFE-AND-DEATH mean?
LIFE-AND-DEATH adjective- Of critical importance to the survival of a living organism.
- Having death as a possible or even likely outcome; perilous.
- Of critical importance to the success of a particular endeavor.