America’s brief: one in Italian outfit would be more fastidious (8)

I believe the answer is:

daintier

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'more fastidious' is the definition.
('dainty' can be similar in meaning to 'fastidious')

'america's brief one in italian outfit' is the wordplay.
'america's brief' becomes 'da' (I can't explain this - if you can you should give a lot more credence to this answer).
'one' becomes 'i' (Roman numeral).
'in' means one lot of letters goes inside another.
'italian outfit' becomes 'Inter' (short for Inter Milan, Italian football team).
'i' put within 'inter' is 'intier'.
'da'+'intier'='DAINTIER'

'would be' acts as a link.

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I've seen this clue in The Times.

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