Composer runs former East German province, largely (7)
I believe the answer is:
rossini
'composer' is the definition.
(Italian composer Gioachino Rossini)
'runs former east german province largely' is the wordplay.
I cannot really see how this works, but
'runs' could be 'r' (cricket abbreviation) and 'r' is found within the answer.
'german' could be 'ossi' (I've seen this before) and 'ossi' is found within the answer.
'province' could be 'ni' (short for Northern Ireland, a province of the UK) and 'ni' is present in the answer.
No letters remain.
This may be the basis of the clue (or it may be nonsense).
Can you help me to learn more?
(Other definitions for rossini that I've seen before include "Great musician" , "Largo al factotum composer" , "Barber of Seville writer" , "he scored regularly" , "Composer of the opera William Tell, d. 1868" .)