An addition that will make a sincere difference (8)
I believe the answer is:
increase
'an addition' is the definition.
(I know that addition can be written as increase)
'a sincere difference' is the wordplay.
'difference' indicates anagramming the letters.
'a'+'sincere'='asincere'
'asincere' anagrammed gives 'INCREASE'.
'that will make' acts as a link.
(Other definitions for increase that I've seen before include "step up" , "Get bigger" , "Grow, expand" , "Wax" , "Profit" .)