Bill having got posh is prohibited (4)
I believe the answer is:
tabu
'is prohibited' is the definition.
('tabu' can be a synonym of 'prohibited')
'bill having got posh' is the wordplay.
'bill' becomes 'tab' (tab is a kind of bill**).
'having got' is a charade indicator (letters next to each other).
'posh' becomes 'u' (abbreviation for upper-class - opposite to non-u).
'tab'+'u'='TABU'
(Other definitions for tabu that I've seen before include "Unacceptable" , "Ban resulting from social custom" , "banned" , "Socially prohibited" , "Social prohibition" .)