Stop on beat: and on criminal! (6)
I believe the answer is:
arrest
'stop' is the definition.
(arrest is a kind of stop)
'on beat and on criminal' is the wordplay.
I cannot quite see how this works, but
'on' could be 're' ('on' can be mean 'with reference to') and 're' is found within the answer.
This explanation may well be incorrect...
Can you help me to learn more?
(Other definitions for arrest that I've seen before include "apprehend a law-breaker" , "Detain under suspicion of criminal behaviour" , "Stop (on suspicion)" , "Stop - detain" , "Sartre (anag) -- check" .)