Article cheers character from Greece (5)
I believe the answer is:
theta
'character from greece' is the definition.
(Greek letter)
'article cheers' is the wordplay.
'article' becomes 'the' (the definite article in English).
'cheers' becomes 'ta' (both can informally mean thank you).
'the'+'ta'='THETA'
(Other definitions for theta that I've seen before include "Foreign character" , "letter to Greeks" , "Letter before iota" , "Foreign letter" , "Letter to the Corinthians" .)