Trendy food shop has to supply food, mostly tasteless (10)
I believe the answer is:
indelicate
'tasteless' is the definition.
('indelicate' can be similar in meaning to 'tasteless')
'trendy food shop has to supply food mostly' is the wordplay.
'trendy' becomes 'in'.
'food shop' becomes 'deli' ('deli' can be a synonym of 'food shop').
'has' means one lot of letters go next to another.
'to supply food' becomes 'cater' ('cater' can be a synonym of 'supply food').
'mostly' means to remove the last letter.
'cater' with its last letter taken off is 'cate'.
'in'+'deli'+'cate'='INDELICATE'
(Other definitions for indelicate that I've seen before include "Coarse" , "lacking taste" , "Practised (a play)" , "Rude - tasteless" , "Rather rude" .)