Briefly applaud south-east Cheshire maybe (6)
I believe the answer is:
cheese
'cheshire maybe' is the definition.
(Cheshire is an example)
'briefly applaud south-east' is the wordplay.
'briefly' means to remove the last letter.
'applaud' becomes 'cheer' (cheering is a kind of applauding).
'south east' becomes 'se'.
'cheer' with its last letter removed is 'chee'.
'chee'+'se'='CHEESE'
(Other definitions for cheese that I've seen before include "Product of milk curds" , "Nautical peaked cap - board with wire attached" , "Food made from milk curds" , "A big one would be important" , "Big one's important" .)