I should add one Greek character (3)
I believe the answer is:
psi
'greek character' is the definition.
(letter from the Greek alphabet)
'i should add one' is the wordplay.
'i should add' becomes 'ps' (as in a PS in a letter).
'one' becomes 'i' (Roman numeral).
'ps'+'i'='PSI'
(Other definitions for psi that I've seen before include "letter from abroad" , "foreign letter" , "Pounds per square inch (abbr.); Greek letter" , "Greek letter; pressure unit" , "Twenty-third letter of Greek alphabet" .)