Gone out chasing cases of criminal activity — constant or moving target? (4,6)
I believe the answer is:
clay pigeon
'moving target?' is the definition.
(target for clay pigeon shooting)
'gone out chasing cases of criminal activity constant' is the wordplay.
'out' indicates an anagram (out can mean wrong or inaccurate).
'chasing' is a charade indicator (letters next to each other).
'cases of criminal activity' becomes 'clay' (I am not sure about this - if you are sure you should believe this answer much more).
'constant' becomes 'pi' (mathematics: a.cy).
'gone' anagrammed gives 'geon'.
'clay'+'pi'='claypi'
'geon' after 'claypi' is 'CLAY PIGEON'.
'or' acts as a link.
Can you help me to learn more?
(Other definitions for clay pigeon that I've seen before include "Moving target" , "Trap shooting target" , "Disc to be shot" , "Disc fired into the air as target for shooting" , "hard bird to shoot?" .)