Large hairpieces worn by important people (7)

I believe the answer is:

bigwigs

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

'worn by important people' is the definition.
'bigwigs' can be an answer for 'people' (bigwig is a kind of person). I am not certain of the 'worn by important' bit.

'large hairpieces' is the wordplay.
'large' becomes 'big' (synonyms).
'hairpieces' becomes 'wigs' (wig is a kind of hairpiece).
'big'+'wigs'='BIGWIGS'

Can you help me to learn more?

I've seen this clue in The Irish Independent.

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