Supposedly conservative style of rebel in US, possibly (4,5)

I believe the answer is:

blue rinse

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'supposedly conservative style' is the definition.
I don't know anything about this answer so I can't tell whether this works.

'rebel in us possibly' is the wordplay.
'possibly' indicates an anagram.
'rebel'+'in'+'us'='rebelinus'
'rebelinus' with letters rearranged gives 'BLUE-RINSE'.

'of' acts as a link.

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I've seen this clue in The Telegraph.

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