New filling for cheese offers solution (5)
I believe the answer is:
brine
'solution' is the definition.
(I know that brine is a type of solution)
'new filling for cheese' is the wordplay.
'new' becomes 'n' (common abbreviation eg NT for New Testament).
'filling for' means one lot of letters goes inside another.
'cheese' becomes 'brie' (Brie is an example).
'n' put inside 'brie' is 'BRINE'.
'offers' acts as a link.
(Other definitions for brine that I've seen before include "Salted water" , "Strong salt-water solution" , "Solution of salt in water" , "preservative" , "pickle" .)