Designer admits fashion finally is sound (7)
I believe the answer is:
channel
'sound' is the definition.
('channel' can be a synonym of 'sound')
'designer admits fashion finally' is the wordplay.
'designer' becomes 'chanel' (Coco Chanel).
'admits' means one lot of letters goes inside another.
'finally' indicates one should take the final letters.
The final letter of 'fashion' is 'n'.
'chanel' placed around 'n' is 'CHANNEL'.
'is' is the link.
(Other definitions for channel that I've seen before include "Groove" , "Seaway south of England" , "Water conduit or TV programme identifier" , "flute" , "Medium of transmission" .)