club and stick, n. — Green’s Dictionary of Slang

club and stick n.

[rhy. sl. = dick n.⁵ (1); the implements are, of course, apposite]

a police officer.

1934		Detective Fiction Weekly (US) 21 Apr. in DU (1949).
1935		A.J. Pollock Und. Speaks 23/1: Clubs and sticks, dicks (detectives).
1944		Maurer & Baker ‘“Aus.” Rhyming Argot’ in AS XIX:3.
1949		Monteleone Criminal Sl. (rev. edn).
1963		L.F. Freed Crime in S. Afr. 106: When he says that he ‘sights’ a ‘club and stick’ or a ‘dick’ he means he sees a detective.