Fast food shop feeding trendy belle on a regular basis (9)
I believe the answer is:
indelible
'fast' is the definition.
(thesaurus)
'food shop feeding trendy belle on a regular basis' is the wordplay.
'food shop' becomes 'deli' ('deli' can be a synonym of 'food shop').
'feeding' means one lot of letters goes inside another.
'trendy' becomes 'in'.
'on a regular basis' means one should take alternating letters.
The alternate letters of 'belle' are 'ble'.
'in'+'ble'='inble'
'deli' inserted within 'inble' is 'INDELIBLE'.
(Other definitions for indelible that I've seen before include "fixed" , "fast" , "not able to be forgotten" , "Of stain, unable to be removed" , "Cannot be removed or erased" .)