No force is necessary to give a supermassive black hole, or anything else, the ability to move through space.
As Newton's Laws of Motion tell us, a body at rest tends to remain at rest, and a body in motion tends to remain in motion, unless it's acted on by some outside force. Since both the star and the black hole are in space, where there's no air and therefore no friction to slow them down, they retain whatever motion they have. The main force affecting them is gravity -- which, in this case, tends to draw them towards each other.
Objects you see in everyday life tend to come to a stop (cars stop moving when they run out of fuel, rolling stones stop rolling, etc.), but that's just because of the force of friction. In an environment like outer space, where there (usually) is no significant friction, bodies in motion can continue in motion for billions of years. Earth continues to spin, the planets continue to orbit around the Sun, and so forth -- not because anything keeps them moving, but because nothing stops them.
And there's no real distinction between rest and motion anyway. All motion is space is defined relative to some other object, or to some defined frame of reference. On Earth, we think of something as being at rest if it's not moving relative to the surface of the Earth. In space, there isn't necessary a single defined frame of reference like that. If two bodies in space are approaching each other, it's equally valid to say that one is moving and the other is at rest, or vice versa, or that they're both moving relative to an observer. That's (part of) the basis of relativity.