They show off straw hats about the start of the season (8)

I believe the answer is:

boasters

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'they show off' is the definition.
The definition suggests an adverb but the answer is not.

'straw hats about the start of the season' is the wordplay.
'straw hats' becomes 'boaters' ('boater' can be a synonym of 'straw hat').
'about' indicates putting letters inside.
'the start of' says to take the initial letters.
The first letter of 'season' is 's'.
'boaters' going around 's' is 'BOASTERS'.

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I've seen this clue in The Irish Independent.

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