Piano song allowed to become a short drama (7)
I believe the answer is:
playlet
'a short drama' is the definition.
(I've seen this in another clue)
'piano song allowed to' is the wordplay.
'piano' becomes 'p' (musical abbreviation).
'song' becomes 'lay' (poetic term for a song).
'allowed to' becomes 'let' (to let something happen is to allow it).
'p'+'lay'+'let'='PLAYLET'
'become' is the link.
(Other definitions for playlet that I've seen before include "Little work" , "Short drama" , "Short scenes" , "Short dramatic piece" , "Minor theatrical work" .)