Daughter in wig perhaps, having dropped an E? (7)
I believe the answer is:
drugged
'dropped an e?' is the definition.
(E can mean an ecstasy pill)
'daughter in wig perhaps' is the wordplay.
'daughter' becomes 'd' (genealogical abbreviation).
'in wig perhaps' becomes 'rugged' (rug can mean a wig).
'd'+'rugged'='DRUGGED'
'having' is the link.
(Other definitions for drugged that I've seen before include "Anaesthetised" , "knocked out" .)