Green’s Dictionary of Slang

hound-dog v.

[hound v. (2)]

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

[US]‘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.
[US]W. Diehl Hooligans (2003) 23: I’ve been hounddogging this mob for what, four, five years?
[UK]Guardian G2 16 July 4: Let’s go hound dogging!