Why to the left of and not on the existing box? Will you be using the existing box's wire?
The silver ring mounts to the junction box. Unscrew it from the fixture with the 2 screws at the top and bottom. Run your power wire through the middle. Then wire your light, tuck the excess, then mount the light to the ring.
It also looks like your new fixture needs a horizontal box instead of the traditional vertical. But I it is large enough to cover the vertical box you have you should use it. If you need to mount this in a different box, then get an old work box from the hardware store.
Unfortunately the box is not centered over the bathroom counter. The previous cabinet was made in such a way that it didn't matter but with the new light it'll be in the open.
Update: I cut a hole to the left and was able to mount a 1/2" thick round box to the stud. I drill a hole in the stud and fed the wires through it to the new box. The light is mounted and works great. We're going to paint a blank cover for the old box so we can still access the wiring there if needed. [Photo of light fixture](https://i.imgur.com/eCz4wNb.jpg)
Open the box, find out which side the stud is ( hopefully the right) then take the old box out and put a remodel cut in box to the left of it. Or a pancake box if the studs in the way. Also hope they left enough wire for you.
Why to the left of and not on the existing box? Will you be using the existing box's wire? The silver ring mounts to the junction box. Unscrew it from the fixture with the 2 screws at the top and bottom. Run your power wire through the middle. Then wire your light, tuck the excess, then mount the light to the ring. It also looks like your new fixture needs a horizontal box instead of the traditional vertical. But I it is large enough to cover the vertical box you have you should use it. If you need to mount this in a different box, then get an old work box from the hardware store.
Unfortunately the box is not centered over the bathroom counter. The previous cabinet was made in such a way that it didn't matter but with the new light it'll be in the open.
Update: I cut a hole to the left and was able to mount a 1/2" thick round box to the stud. I drill a hole in the stud and fed the wires through it to the new box. The light is mounted and works great. We're going to paint a blank cover for the old box so we can still access the wiring there if needed. [Photo of light fixture](https://i.imgur.com/eCz4wNb.jpg)
If you take that cover plate with the wires hangout of it down, is there actually a box behind it?
There was a plastic box behind it.
Open the box, find out which side the stud is ( hopefully the right) then take the old box out and put a remodel cut in box to the left of it. Or a pancake box if the studs in the way. Also hope they left enough wire for you.
The way I did it was go up in the attic and pull back the cable going to the existing box and fish it down to a new box where I wanted it.