Popular copper entertains them periodically, beyond a doubt (13)
I believe the answer is:
incontestable
'beyond a doubt' is the definition.
(something incontestable is beyond all doubt)
'popular copper entertains them periodically' is the wordplay.
I cannot quite see how this works, but
'popular' could be 'in' ('in' can mean trendy) and 'in' is found within the answer.
The remaining letters 'contestable' is a valid word which might be clued in a way I don't understand.
This may be the basis of the clue (or it may be nonsense).
(Other definitions for incontestable that I've seen before include "Without doubt" , "Beyond dispute" , "sure" .)