A bit of luck for detectives, that's clear (5)
I believe the answer is:
lucid
'clear' is the definition.
(similar in meaning)
'a bit of luck for detectives' is the wordplay.
'a bit of luck for' becomes 'lu' (I can't justify this - if you can you should give a lot more credence to this answer).
'detectives' becomes 'CID' (abbreviation for Criminal Investigation Department).
'lu'+'cid'='LUCID'
'that's' acts as a link.
Can you help me to learn more?
(Other definitions for lucid that I've seen before include "Bright; sane" , "Clear, intelligible" , "Rational, clear" , "Clear, easily understandable" , "Quite clear" .)
