One reason to visit the National Gallery would be to write music! (6)
I believe the answer is:
notate
'to write music' is the definition.
(I've seen this in another clue)
'one reason to visit the national gallery' is the wordplay.
'one reason' becomes 'o' (I can't explain this - if you can you should believe this answer much more).
'to visit' is an insertion indicator.
'the national' becomes 'n' (abbreviation listed in Chambers).
'gallery' becomes 'tate' (Tate Modern, Tate Britain etc).
'n'+'tate'='ntate'
'o' inserted into 'ntate' is 'NOTATE'.
'would be' is the link.
Can you help me to learn more?
(Other definitions for notate that I've seen before include "Mark up" , "Put down in symbols" , "Record in bars" , "Express in symbols" , "Write symbolically" .)