Shop of fine appearance? Not half (4)
I believe the answer is:
deli
'shop' is the definition.
(I've seen this before)
'of fine appearance? not half' is the wordplay.
'of fine appearance?' becomes 'delicate'.
'not half' means to take half the letters.
'delicate' with half the letters taken is 'DELI'.
(Other definitions for deli that I've seen before include "Fine foods shop" , "Specialised food shop" , "Exotic food shop" , "Special shop" , "Unusual food shop" .)