Hold not with the hounds and run with the hare.

The saying rebukes divided loyalty: a person cannot honestly support one side while also helping its opponent. In the hunting image, siding with the hounds while fleeing with the hare represents trying to profit from both camps.

It is especially apt when someone publicly claims one allegiance but privately acts for the opposing interest. It implies deliberate, self-serving inconsistency rather than the ordinary balancing of different responsibilities, and so can portray the person as unreliable.

Use it to criticize apparent double-dealing in a dispute, rivalry, or negotiation where interests directly conflict. Its older negative phrasing gives it a proverbial, somewhat formal tone; because it can sound accusatory, reserve it for clear cases and explain the hunting image if needed.