Short cut that's taken by copper (5)
I believe the answer is:
bobby
'copper' is the definition.
(I know that copper can be written as bobby)
'short cut that's taken by' is the wordplay.
'short cut' becomes 'bob' (I have seen 'Short cut' mean 'bob' so perhaps 'cut' could also mean 'bob'; 'short' asks for an abbreviation).
'that's taken' is a charade indicator (letters next to each other).
'bob'+'by'='BOBBY'
(Other definitions for bobby that I've seen before include "Policeman (sl.)" , "Policeman (colloq.)" , "Peeler" , "- Moore, World Cup winning captain" , "Policeman; man's name" .)