Doing extra obfuscated personal reason to get involved (3,2,5)

I believe the answer is:

axe to grind

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'get involved' is the definition.
I don't know anything about this answer so I can't judge whether this works.

'doing extra obfuscated personal reason' is the wordplay.
'doing extra' anagrams to 'AXE TO GRIND'.
Though, I'm not sure how the anagram is indicated.

'to' is the link.

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I've seen this clue in The Times.

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