Law court run by Greek character initially (4,3)
I believe the answer is:
riot act
'law' is the definition.
(Riot Act is an example)
'court run by greek character initially' is the wordplay.
'court' becomes 'ct'.
'run' becomes 'r' (cricket abbreviation).
'by' is a charade indicator (letters next to each other).
'greek character' becomes 'iota' (letter from the Greek alphabet**).
'initially' is a charade indicator (letters next to each other).
'r'+'iota' is 'riota'.
'ct' put after 'riota' is 'RIOT ACT'.
(Other definitions for riot act that I've seen before include "Citator of law concerning public affray" , "used to deal with unrest" , "designed to nip trouble in the bud" , "Old law designed to disperse a mob" , "Statute against rowdy behaviour" .)