Museum of London houses royal gallery (7)
I believe the answer is:
veranda
'gallery' is the definition.
(synonyms)
'museum of london houses royal' is the wordplay.
'museum of london' becomes 'vanda' (I can't explain this - if you can you should give a lot more credence to this answer).
'houses' means one lot of letters goes inside another.
'royal' becomes 'er' (abbreviation for Elizabeth Regina).
'vanda' enclosing 'er' is 'VERANDA'.
Can you help me to learn more?
(Other definitions for veranda that I've seen before include "Roofed platform along the outside of a house" , "Open roofed platform" , "Porch along the outside of a building" , "Open portico" , "balcony" .)