Crossword Genius

Irritate rising head with much questioning (6,4)

Ross

I believe the answer is:

gallup poll

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'much questioning' is the definition.
The definition suggests a singular noun which matches the answer.

'irritate rising head' is the wordplay.
'irritate' becomes 'gall' (galling is a kind of irritating).
'rising' becomes 'up' (similar in meaning).
'head' becomes 'poll' (poll is a now rare word for head or scalp).
'gall'+'up'+'poll'='GALLUP POLL'

'with' is the link.

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I've seen this clue in the Sydney Morning Herald.
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