Wander aimlessly, having unusual gravitas (8)

I believe the answer is:

stravaig

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

'unusual gravitas' is the wordplay.
'unusual' indicates anagramming the letters.
'gravitas' is an anagram of 'STRAVAIG'.

'having' acts as a link.

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I've seen this clue in The Times.

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