Fast food store feeding popular belle regularly (9)
I believe the answer is:
indelible
'fast' is the definition.
(I've seen this before)
'food store feeding popular belle regularly' is the wordplay.
'food store' becomes 'deli' (I've seen this in other clues).
'feeding' indicates putting letters inside.
'popular' becomes 'in' ('in' can mean trendy).
'regularly' means one should take alternating letters (regularly take one letter, leave next etc.).
The alternating letters of 'belle' are 'ble'.
'in'+'ble'='inble'
'deli' inserted into 'inble' is 'INDELIBLE'.
(Other definitions for indelible that I've seen before include "fast" , "not able to be forgotten" , "Permanent" , "fixed" , "Cannot be removed or erased" .)