Eatery in Corsica regularly hosting a gala (9)
I believe the answer is:
cafeteria
'eatery' is the definition.
(I know that cafeteria is a type of eatery)
'corsica regularly hosting a gala' is the wordplay.
'regularly' means one should take alternating letters (regularly take one letter, leave next etc.).
'hosting' indicates putting letters inside (inserted letters are welcomed in or hosted).
'gala' becomes 'fete' (both can mean a festive event).
The alternating letters of 'corsica' are 'cria'.
'a'+'fete'='afete'
'cria' placed around 'afete' is 'CAFETERIA'.
'in' acts as a link.
(Other definitions for cafeteria that I've seen before include "Canteen" , "Self-service eatery" , "where food is served" , "Self-help facility" , "Self-service restaurant" .)