Manage to lose tail — police officer (3)
I believe the answer is:
cop
'police officer' is the definition.
(cop is a kind of police officer)
'manage to lose tail' is the wordplay.
'manage' becomes 'cope' (manage can mean to cope or do well).
'to lose tail' means to remove the last letter (I've seen 'losing tail' mean this).
'cope' with its last letter removed is 'COP'.
(Other definitions for cop that I've seen before include "An American policeman" , "busy" , "Policeman (informal)" , "catch" , "Policeman (sl)" .)