A gyroscope produces only angular momentum, not thrust. But even then, all motion is conserved. To spin something, you need to apply an opposite force. If I spin a top, I would have to apply a force that would make me spin the other direction if I couldn’t use the friction of the ground against my shoes to stop me. Conservation of momentum means that for every object set in motion, it is balanced by another object, so that the net result amounts to zero.
call it a scientist's hobby...