There appears to be some confusion on how to get the 3 piece ring. I haven't seen it explained anywhere, so here goes...

To get the 3 piece elite ring, wear the 3 elite pieces, then talk to the fallen prince. The 1st time you talk to him, he gives you the 2 piece ring. Talk to him again, and he gives you the 3 piece ring.

Now equip, and enjoy.