Crossword Genius

VIP presumably having a large head? (6)

Ross

I believe the answer is:

bigwig

I'm a little stuck... Click here to teach me more about this clue!

'vip' is the definition.
(I've seen this before)

'presumably having a large head?' is the wordplay.
I cannot quite see how this works, but
'large' could be 'big' (synonyms) and 'big' is found in the answer.
The remaining letters 'wig' is a valid word which might be clued in a way I don't see.
This may be the basis of the clue (or it may be nonsense).

Can you help me to learn more?

(Other definitions for bigwig that I've seen before include "Important person (slang)" , "Person of some importance" , "Dignitary (sl.)" , "VIP with large toupee" , "What may lie ahead largely" .)

I've seen this clue in the Evening Standard.
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