VIP with a swollen head, presumably (6)
I believe the answer is:
bigwig
'vip' is the definition.
(I've seen this in another clue)
I don't understand how the remainder of the clue works.
Can you help me to learn more?
(Other definitions for bigwig that I've seen before include "Somebody" , "Important person (slang)" , "Mogul" , "Important person with large toupee" , "VIP with large toupee" .)