If testing includes an aspect of personality (9)

I believe the answer is:

providing

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'if' is the definition.
I can't judge whether this definition defines the answer.

'testing includes an aspect of personality' is the wordplay.
'testing' becomes 'proving' ('prove' can be a synonym of 'test').
'includes' means one lot of letters goes inside another.
'an aspect of personality' becomes 'id' (I am not sure about this - if you are sure you should give a lot more credence to this answer).
'proving' enclosing 'id' is 'PROVIDING'.

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I've seen this clue in The Guardian.

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