His men ordered to accept a measure of devotion to Greek culture (9)
I believe the answer is:
hellenism
'devotion to greek culture' is the definition.
(term for the study of Greek culture)
'his men ordered to accept a measure' is the wordplay.
'ordered' indicates anagramming the letters.
'to accept' means one lot of letters goes inside another.
'a measure' becomes 'ell' (historical unit of length).
'his'+'men'='hismen'
'hismen' is an anagram of 'henism'.
'henism' going around 'ell' is 'HELLENISM'.
'of' acts as a link.
(Another definition for hellenism that I've seen is " Greek culture".)