The Great Attractor is a hypothesized gravity source that is causing the movement of our own local cluster. If it exists, it is hidden from our view by the center of our own galaxy.
However, I don’t think gravity is responsible for large scale movements in the universe; it’s just not strong enough to contradict the expansion of space, which is the prime mover.
My hypothesis for the measured movement of our cluster is that the movement is left over from the great annihilation period. Two chain reaction bubbles collided to form this cluster, but one bubble had more expansion power than the other. So forever more, this entire cluster will continue to drift in the direction of the bubble with the weaker expansion force.
There is no gravity source moving our cluster. Our cluster is just a chunk of filament that never quite stopped moving from that initial event.
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Astronomers have recently detected an entire filament of galaxies, that is collectively orbiting a common axis. That is not only surprising, but is entirely implausible, in the Standard Model. There is absolutely no mechanism for this movement.
Admittedly, I didn't predict this movement, but it is at least understandable, within the Big Split model. Since filaments are long islands of matter (or antimatter) that are caught between expanding spacetime bubbles, it's easy to imagine that such an island was spun by two well-placed bubbles, one on each side, which rub up against the filament, and get it to spin, relative to the void space around it.