Important person's large hairpiece (6)
I believe the answer is:
bigwig
'important person's' is the definition.
(bigwig is a kind of important person)
'large hairpiece' is the wordplay.
'large' becomes 'big' (synonyms).
'hairpiece' becomes 'wig' (wig is a kind of hairpiece).
'big'+'wig'='BIGWIG'
(Other definitions for bigwig that I've seen before include "Important person with large toupee" , "Personage" , "What may lie ahead largely" , "Dignitary (sl.)" , "Luminary" .)