Having authority, detectives are calm (6)
I believe the answer is:
placid
'are calm' is the definition.
(similar in meaning)
'having authority detectives' is the wordplay.
'having authority' becomes 'pla' (I can't justify this - if you can you should give a lot more credence to this answer).
'detectives' becomes 'cid'.
'pla'+'cid'='PLACID'
Can you help me to learn more?
(Other definitions for placid that I've seen before include "Tranquil, unruffled" , "Calm of nature" , "Unconcerned" , "Peaceful and tranquil" , "Tranquil, even-tempered" .)