A small fear - could be an unnecessary alert (5,5)

I believe the answer is:

false alarm

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'an unnecessary alert' is the definition.
The definition suggests a singular noun which matches the answer.

'a small fear could be' is the wordplay.
'could be' indicates an anagram.
'a'+'small'+'fear'='asmallfear'
'asmallfear' is an anagram of 'FALSE ALARM'.

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(Other definitions for false alarm that I've seen before include "unfounded scare?" , "Warning proving unnecessary" , "Panic over" .)

I've seen this clue in The Irish News.

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