Supporters mostly run restaurant (9)
I believe the answer is:
brasserie
'restaurant' is the definition.
(brasserie is a kind of restaurant)
'supporters mostly run' is the wordplay.
'supporters' becomes 'bras' (a bra gives support to breasts).
'mostly' means to remove the last letter.
'run' becomes 'series' (both can mean a sequence of things).
'series' with its last letter removed is 'serie'.
'bras'+'serie'='BRASSERIE'
(Other definitions for brasserie that I've seen before include "Small restaurant serving alcohol as well as food" , "French restaurant" , "eatery" , "French-style restaurant" , "bar serving food" .)