Old police tests brought up by institute (5)
I believe the answer is:
stasi
'old police' is the definition.
(former secret police of East Germany)
'tests brought up by institute' is the wordplay.
'tests' becomes 'sats' (exams taken in UK schools).
'brought up' shows that the letters should be reversed in order (down clues only).
'by' means one lot of letters go next to another.
'institute' becomes 'i' (common abbreviation as in MIT).
'sats' written backwards gives 'stas'.
'stas'+'i'='STASI'
(Other definitions for stasi that I've seen before include "Force behind Wall" , "Former security force" , "Former German security service" , "East German Secret Police" , "old secret service" .)