Close match (5,5)
I believe the answer is:
local derby
'close match' is the definition.
(a sports match between local rivals)
'close match' is the wordplay.
'close' becomes 'local' (I am not sure about this - if you are sure you should believe this answer much more).
'match' becomes 'derby' (I have seen 'local match' mean 'derby' so perhaps 'match' could also mean 'derby').
'local'+'derby'='LOCAL DERBY'
(Other definitions for local derby that I've seen before include "Competition between two close teams" , "grudge match?" , "Meeting of neighbours" , "Match between nearby teams" , "Nearby game?" .)