VIP with at least one major overhead (6)
I believe the answer is:
bigwig
'vip' is the definition.
(I've seen this in another clue)
'with at least one major overhead' is the wordplay.
'with' becomes 'w' (abbreviation).
'at least one' becomes 'ig' (I can't justify this - if you can you should give a lot more credence to this answer).
'major' becomes 'big' (I've seen this in other clues).
'overhead' means one lot of letters go next to another (in a down clue, some letters go over others).
'w'+'ig'='wig'
'wig' after 'big' is 'BIGWIG'.
Can you help me to learn more?
(Other definitions for bigwig that I've seen before include "Somebody" , "'Chief, top banana (6)'" , "Mogul" , "Important person with large toupee" , "Important person (slang)" .)