Base display of arrogance greeting native American (7)

I believe the answer is:

airshow

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'arrogance greeting native american' is the definition.
I know nothing about this answer so I can't tell whether it can be defined by this definition.

'base display' is the wordplay.
'base' becomes 'air base' (air base is a kind of base).
'display' becomes 'show' (synonyms).
'air'+'show'='AIRSHOW'

'of' is the link.

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I've seen this clue in The Times.

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