Bag from fringes of Carnaby Street (4)
I believe the answer is:
cyst
'bag' is the definition.
(I've seen this before)
'fringes of carnaby street' is the wordplay.
'fringes of' says to hollow out the word (remove centre letters).
'street' becomes 'st' (abbreviation).
'carnaby' with its middle taken out is 'cy'.
'cy'+'st'='CYST'
'from' is the link.
(Other definitions for cyst that I've seen before include "Bag-like growth containing diseased matter" , "Abnormal membranous sac" , "pouch" , "Sac in the body containing liquid secretion" , "Abnormal closed sac in a body" .)