All-important fault-finding (8)

I believe the answer is:

critical

I believe this is a double definition.

'all-important' is the first definition.
(I've seen this before)

'fault-finding' is the second definition.
(I've seen this before)

(Other definitions for critical that I've seen before include "Finding faults" , "Decisively important" , "essential" , "Urgent - fault-finding" , "Urgent or carping" .)

I've seen this clue in The Guardian.

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