Presided over police department that's rotten (6)

I believe the answer is:

rancid

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'that's rotten' is the definition.
(I've seen this before)

'presided over police department' is the wordplay.
'presided over' becomes 'ran' (I can't justify this - if you can you should believe this answer much more).
'police department' becomes 'CID' (abbreviation for Criminal Investigation Department).
'ran'+'cid'='RANCID'

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(Other definitions for rancid that I've seen before include "Foul-tasting" , "Stinking" , "Unpleasantly stale" , "Rank-smelling." , "(Of butter) stale" .)

I've seen this clue in The Independent.

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