Composer didn't have 'unfinished', with end of symphony penned (5)
I believe the answer is:
haydn
'composer' is the definition.
(I know that Haydn is a composer)
'unfinished with end of symphony penned' is the wordplay.
'unfinished' becomes 'han' (I can't justify this - if you can you should give a lot more credence to this answer).
'with' is an insertion indicator.
'end of' suggests the final letters.
The final letters of 'symphony penned' are 'yd'.
'han' going around 'yd' is 'HAYDN'.
'didn't have' acts as a link.
I am not very happy about this link. Some or all of it may belong to another bit of the clue.
Can you help me to learn more?
(Other definitions for haydn that I've seen before include "Austrian symphonist, d. 1809" , "Esterhazy composer" , "Joseph -, prolific eighteenth to nineteenth century Austrian composer" , "Creation composer" , "Composer of over 100 symphonies" .)