That is a cast iron closet ring, probably 4 x 2 over 4" cast iron pipe. 4x4 and 4 x 6 are also available which would allow you to raise the ring up to 4 inches. You can see a ring of lead between the inside of flange and the outside of the pipe. If that is drilled the lead can be pried out and also the oakum under it. A plumber would have that old ring out in a jiffy, perhaps using a more dramatic method that I won't even mention. There is lead holding the ring in place but it won't kill you, just wash your hands - which I assume you would do after playing with sewer pipe anyway. The best thing is to then put in a spacer around the pipe that you can run the new floor up to, often cardboard is used. Pre-made spacers are available. When the floor is finished the spacer is removed and the new longer ring dropped into place. The flange will sit on the floor and be fastened to it. I suspect you will want a plumber to caulk in the new ring because it involves oakum and molten lead. There is a powder you can mix with water as a substitute for the lead, Soil-O by Black Swan. There are also rings that clamp onto the outside of the pipe but that would involve chipping cement (and, hopefully, not the pipe). They also tend to be more difficult to fasten to the floor because of the way they are made. Best practice is to then add a short piece of 4" pipe that sits on top of the existing pipe and rises to the top top of the flange so there is no shoulder for stuff to get hung up on. This true of both the caulk and "instant-set" rings. Plastic pipe is fine for this and the space around the outside can be packed with oakum to hold it centered. I have even heard of plumber's putty being used for this. There are also rings that push into the 4" pipe and seal with rubber. If the cast iron is not smooth (which it won't be) that is at times an issue. And, of course there are various extensions. Those are pretty much your options.