Majestic gallery with cunning exterior (7)
I believe the answer is:
stately
'majestic' is the definition.
(I've seen this in another clue)
'gallery with cunning exterior' is the wordplay.
'gallery' becomes 'tate' (Tate Modern, Tate Britain etc).
'with cunning' becomes 'sly' (synonyms. I am not sure about the 'with' bit.).
'exterior' means one lot of letters goes inside another.
'tate' going into 'sly' is 'STATELY'.
(Other definitions for stately that I've seen before include "August" , "Grand, dignified" , "Imperial" , "` `In Xanadu did Kubla Khan / A ....... pleasure-dome decree' ' (Coleridge)" , "Formal; type of home" .)