Tart shop’s beginning to advertise (8)
I believe the answer is:
strumpet
'tart' is the definition.
(I've seen this before)
'shop's beginning to advertise' is the wordplay.
'beginning to' indicates taking the first letters.
'advertise' becomes 'trumpet' (to trumpet something is to advertise it).
The initial letter of 'shops' is 's'.
's'+'trumpet'='STRUMPET'
(Other definitions for strumpet that I've seen before include "... unlike her!" , "Whore" , "Trumpets for loose woman" , "Tart" , "Harlot" .)