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Considering a gravitational coupling between the spin and the orbital angular momentum of a spinning test particle orbiting a central massive body, we derive two particular consequences: (1) the influence of the coupling on the location of the innermost stable circular orbit and (2) the gravitomagnetic clock effect due to this coupling. The previous result does not seem to exist for the former, while for the latter we arrive at a result that coincides with what we think is the most accurate.