Greek character reportedly regarded as drunk (3-4)
I believe the answer is:
pie-eyed
'drunk' is the definition.
(I've seen this before)
'greek character reportedly regarded' is the subsidiary indication.
'greek character' becomes 'pi'.
'reportedly' shows a homophone (sound like).
'regarded' becomes 'eyed' (I've seen this in other clues).
'pi' is a homophone of 'pie'.
'pie'+'eyed'='pieeyed'
'as' is the link.
(Other definitions for pie-eyed that I've seen before include "Very drunk (colloq.)" , "Blotto" .)