This term is used in various different meanings. Castaneda uses this in reference to the warrior's virtues of forebearance and timing. The meaning of waiting for the opening implied by stalking becomes quite clear in the context of the petty tyrant, see separate article.
The term implies however more than hunter's skill and patience in relation to an external situation. The same or similar approach can be taken towards the internal predator. One can deliberately irritate this part of self by denying to give in to its habits and demands. The 'predator's mind' becomes quite obvious under stress.
The term is also sometimes used to describe what the 'control system' or 'matrix' does in relation to humanity. The cosmic predator stalks humanity, setting it up and keeping it stressed, keeping it in reacting mode, faced with constant new crisis so as to stay one step ahead and elicit a predictable emotional reaction, as from an animal stalked by a predator. Fomenting wars, various tactics of divide and conquer and economic manipulation are examples of this. These should not be seen as the direct work of the alien predatory presence but these do play into the hands of 4D STS.