Brown back in period of decline (8)
I believe the answer is:
stagnate
'decline' is the definition.
(I've seen this before)
'brown back in period' is the wordplay.
'brown' becomes 'tan' (tan is a kind of brown).
'back' shows that the letters should be reversed in order.
'in' means one lot of letters goes inside another.
'period' becomes 'stage' (e.g. a stage in history).
'tan' written backwards gives 'nat'.
'nat' put into 'stage' is 'STAGNATE'.
'of' is the link.
(Other definitions for stagnate that I've seen before include "turn foul" , "Be idle" , "Become still or stale through inactivity" , "Make no move" , "Fester" .)