It is highly unlikely that there would be clips to hold it to under sink plumbing because the plumbing is not part of the cabinet and there's no telling where pipes might be.
Much more likely is that it's supposed to be screwed into the left-side wall or that it's supposed to be screwed down through the floor of the cabinet itself.
I'd suggest looking at the ends of the board to see if there are holes for screws, or look at the other long edge (away from camera) for screw holes, as there don't appear to be any on the long edge toward camera.
If you don't find any existing holes, then you can make your own by drilling holes for screws then driving screws into your holes. You will want to drill pilot holes as particle board (which this is made of) can easily swell and split from trying to drive a screw into it without a pilot hole.
For the simple purpose of holding this toe kick in place, darn near any screw will do - this isn't a structural piece, it just needs 2 or 3 screws evenly spaced across its length to hold it there. If this were a structural piece, you'd want screws specifically for particle board.