The rest stay with the Berliner (9)
I believe the answer is:
'the rest' is the definition.
'stay with the berliner' is the wordplay.
'stay' becomes 'remain' (synonyms).
'with' means one lot of letters go next to another.
'the berliner' becomes 'der' (I am not sure about this - if you are sure you should give a lot more credence to this answer).
Can you help me to learn more?
(Other definitions for remainder that I've seen before include "Dispose of unsold books cheaply" , "Left-over" , "Balance" , "Dispose of unsold copies of book at a reduced price" , "The part that is left over" .)