A depression in case of locals getting grants (6)
I believe the answer is:
allows
'grants' is the definition.
('allow' can be a synonym of 'grant')
'a depression in case of locals' is the wordplay.
'depression' becomes 'low' ('low' can be a synonym of 'depression'**).
'in' means one lot of letters goes inside another.
'case of' says to hollow out the word (remove centre letters) (outsides of).
'locals' with its centre taken out is 'ls'.
'low' inserted into 'ls' is 'llows'.
'a'+'llows'='ALLOWS'
'getting' is the link.
(Other definitions for allows that I've seen before include "Sallow (anag.)" , "Grants leave" , "Permits to do something" , "Gives permission" , "Tolerates" .)