One month besieging Brown Sector (6)
I believe the answer is:
octant
'sector' is the definition.
(one of eight sectors in something)
'one month besieging brown' is the wordplay.
'one month' becomes 'Oct' (abbreviation for October).
'besieging' indicates putting letters inside.
'brown' becomes 'tan' (tan is a kind of brown).
'oct' placed around 'tan' is 'OCTANT'.
(Other definitions for octant that I've seen before include "Device to measure angles to a celestial body" , "Eighth part of circle" , "segment of disc" , "45 degrees" .)