Brown's back keeping English cool (4)
I believe the answer is:
neat
'cool' is the definition.
('neat' can be a synonym of 'cool')
'brown's back keeping english' is the wordplay.
'brown' becomes 'tan' (tan is a kind of brown).
'back' says the letters should be written backwards.
'keeping' indicates putting letters inside.
'english' becomes 'e' (abbreviation).
'tan' written backwards gives 'nat'.
'nat' going around 'e' is 'NEAT'.
(Other definitions for neat that I've seen before include "pat?" , "Excellent American" , "avoiding water?" , "lacking water" , "Tidy - old cow!" .)