Area, local authority district, gets grant (5)
I believe the answer is:
award
'grant' is the definition.
(I know that grant can be written as award)
'area local authority district' is the wordplay.
'area' becomes 'a' (maths abbreviation).
'local authority district' becomes 'ward' (as in council wards).
'a'+'ward'='AWARD'
'gets' acts as a link.
(Other definitions for award that I've seen before include "Trophy or medal, for example" , "Prize in recognition of achievement" , "certificate?" , "Decoration" , "Tony, say" .)