Ordinary clothes possibly fit on Greek character (5)
I believe the answer is:
mufti
'ordinary clothes' is the definition.
(I've seen this in another clue)
'possibly fit on greek character' is the wordplay.
'possibly' is an anagram indicator.
'on' says to put letters next to each other.
'greek character' becomes 'mu' (letter from the Greek alphabet).
'fit' anagrammed gives 'fti'.
'fti' put after 'mu' is 'MUFTI'.
(Other definitions for mufti that I've seen before include "Plain clothes worn by soldier" , "Civilian clothes worn by service personnel" , "Civvies; Muslim legal expert" , "Non-military clothing" , "officer of the law" .)