For the remainder, a fresh rise is expected (7)
I believe the answer is:
residue
'for the remainder' is the definition.
(residue means a remainder or remains)
'a fresh rise is expected' is the wordplay.
'a fresh' indicates anagramming the letters.
'is expected' becomes 'due' (similar in meaning).
'rise' with letters rearranged gives 'resi'.
'resi'+'due'='RESIDUE'
(Other definitions for residue that I've seen before include "Something left over" , "What remains of something" , "It remains after other parts have been taken away" , "rest" , "waste" .)