Drastically alter letter from Greek gallery (6)
I believe the answer is:
mutate
'drastically alter' is the definition.
'letter from greek gallery' is the wordplay.
'letter from greek' becomes 'mu' (letter of the Greek alphabet).
'gallery' becomes 'tate' (Tate Modern, Tate Britain etc).
'mu'+'tate'='MUTATE'
(Other definitions for mutate that I've seen before include "Change into a variant form" , "Gradually change form" , "Change genetically" , "Undergo alteration in form" , "Convert" .)