Appealing to reduce noise at the back (4)
I believe the answer is:
cute
'appealing' is the definition.
(I've seen this before)
'reduce noise at the back' is the wordplay.
'reduce' becomes 'cut' (synonyms).
'at the back' indicates one should take the final letters.
The last letter of 'noise' is 'e'.
'cut'+'e'='CUTE'
'to' is the link.
(Other definitions for cute that I've seen before include "Attractive and quaint (4" , "Quaintly pleasing" , "Small, delightful" , "Shrewd" , "Smart" .)