Green’s Dictionary of Slang

to go out looking for a (sexual) companion or criminal.

1959		‘Monroe Fry’ Sex, Vice & Business 97: Last year Philadelphia was rocked by a sensational case [. . . .] Out of the evidence came the story of sex orgies at a secluded estate aptly named Hound Dog Hill.
1984		W. Diehl Hooligans (2003) 23: I’ve been hounddogging this mob for what, four, five years?
1999		Guardian G2 16 July 4: Let’s go hound dogging!