Change Greek character with brief thank-you note (6)
I believe the answer is:
mutate
'change' is the definition.
(mutating is a kind of changing)
'greek character with brief thank-you note' is the wordplay.
'greek character' becomes 'mu' (letter from the Greek alphabet).
'with' means one lot of letters go next to another.
'brief thank you' becomes 'ta'.
'note' becomes 'te' (musical note).
'mu'+'ta'+'te'='MUTATE'
(Other definitions for mutate that I've seen before include "Change into something different" , "effect major change" , "(In genetics) change" , "Convert" , "Undergo change to another form" .)