Second piano study to become broader (6)
I believe the answer is:
spread
'become broader' is the definition.
(spread can mean to become broader)
'second piano study' is the wordplay.
'second' becomes 's' (common abbreviation).
'piano' becomes 'p' (musical abbreviation).
'study' becomes 'read' (synonyms).
's'+'p'+'read'='SPREAD'
'to' acts as a link.
(Other definitions for spread that I've seen before include "Expanse; edible paste" , "Soft paste; large meal" , "Broadcast" , "Open, fan out, unfold" , "we hope to avoid in middle age" .)