Greek character that looks different around the East (5)
I believe the answer is:
theta
'greek character' is the definition.
(letter from the Greek alphabet)
'that looks different around the east' is the wordplay.
'looks different' indicates anagramming the letters (I've seen 'looking different' mean this (I've seen this in other clues)).
'around' indicates putting letters inside.
'the east' becomes 'E' (synonyms).
'that' with letters rearranged gives 'thta'.
'thta' enclosing 'e' is 'THETA'.
(Other definitions for theta that I've seen before include "Make amends for" , "Greek letter used in trigonometry" , "Letter before iota" , "Letter to the Corinthians" , "classic character?" .)