What you may call a bigwig with LSD or rolling joint (8)
I believe the answer is:
lordship
'what you may call a bigwig' is the definition.
(your lordship)
'lsd or rolling joint' is the wordplay.
'rolling' is an anagram indicator.
'joint' becomes 'hip joint' (part of body).
'lsd'+'or'='lsdor'
'lsdor' is an anagram of 'lords'.
'lords'+'hip'='LORDSHIP'
'with' acts as a link.
(Other definitions for lordship that I've seen before include "House" , "Supreme power" , "Dominion - authority" , "Superior state" , "Supreme rule" .)