High time embracing Greek character's dance (6)
I believe the answer is:
minuet
'dance' is the definition.
(minuet is a kind of dance)
'high time embracing greek character's' is the wordplay.
'high' is an anagram indicator (can mean drunk or on drugs and hence disordered).
'embracing' indicates putting letters inside.
'greek character' becomes 'nu' (letter from the Greek alphabet).
'time' is an anagram of 'miet'.
'miet' placed around 'nu' is 'MINUET'.
(Other definitions for minuet that I've seen before include "Stately court dance" , "Stately C 18 dance" , "Stately old dance, takes only a minute" , "Gracious old dance, just takes a minute" , "Slow, graceful dance" .)