Predators, as I see it, are not the same as psychopaths. Psychopaths have a defective and more or less untrainable empathetic function. Predators on the other hand can read their victims empathetically to their own advantage. They see no moral problem in dealing with their instinctive needs as predators - just as other humans generally see no problem with the necessity of killing animals to eat.
Psychopaths however just don’t see moral rules as understandable. They learn to mimic the expected behaviors, but don’t feel, either fully or at all, the emotionally learned responses that otherwise would govern that morality.
And so we have some psychopaths that are born without the emotional capacity to read the signals that humans (among other animals) in a cooperative setting have evolved to send each other instructively.
And even if there are some psychopaths that can learn to read the signs, they will lack the capacity to be concerned with the implied instructions. Essentially, these psychopaths prefer to use deceptive strategies, not understanding the “mechanics” of attaining trust. Predators however do understand the importance of trust, and very often will form such trusting bonds with potential prey in an environment where the need for predatory strategies has been suspended; where their instinctive strategies, however, will still be there to depend on if circumstances change.
Further, predators in predatory groups will trust each other to obey the rules of predatory society that they’ve been born to learn and understand. And while there can also be such a thing as a psychopathically oriented group (nomadic gypsies may be a good example), no such group comprised solely of psychopathic individuals has been successfully evolved or developed to my knowledge.
As to fear of immediate consequences, psychopaths, who could not win the trust of this type of predatory enemy, would not know how to negotiate their way out of an immediate threat from this type of adversary. The expectation of some immediate damage would likely trigger an instinctive fight or flight response.
But their predators will tend to make more practical use of the effects of fear. If a fight with a psychopath resulted, both sides of the conflict would attempt to fearlessly deceive the other; but the predators, who can generally read their prey much better than the prey can read them, would have the advantage - especially where the prey were psychopathic and unable to use their limited emotional strategies properly. That psychopath, fearing the finality of becoming a figurative meal, would likely run.So yes, you can be a predatory psychopath or a psychopathic predator, but again, the essential differences remain the same. Predators have functional purposes while psychopaths must serve dysfunctional ones.
(And as a PI, I was always a predator as far as my working strategies were concerned.)