Spoiler: My Teresa is the 3rd being theory
showEvidence(or points that i think support my argument in this case)
Point 1) Clare originally brought Teresa's head into the organization and asked them to "put Teresa inside of her". Which is rather ironic if my theory has any truth to it.
Point 2) In chapter 103 there was a flash of the memory Priscilla has been trying to recall. It was a woman holding a sword over a headless body, but she couldn't remember the face. At the end of that chapter she concludes that her desire is to kill her "one more time". Any way i look at that statement it's can't be talking about Clare. The woman holding the sword was Priscilla herself and the headless body was Teresa. Clare wasn't even in that memory.
The conclusion i draw from this memory sequence is that what Priscilla is unable to remember is that she herself was the one she wanted to destroy. Her last memory as a human was probably Teresa offering to kill her; and remember what Irene said about her way back in chapter 18 "she hates Yoma more than anyone". Which is why i think she has been instinctively seeking Teresa's "scent".
If there is enough of Teresa in Clare to for Priscilla to find then there might just be enough to bring her back.
Point 3) As things stand Clare herself has only the upper half of body left, and she isn't a defensive type so the lower half is not going to grow back by normal means(seems weird to call that "normal"). If a body is going to have to be reconstructed for Clare somehow, it seems reasonable to think that maybe one could theoretically be created for Teresa through the same method.
Point 4) If Rafaela's consciousness could be reconstructed inside that mass of Yoki and Yoma power from nothing but a fragmented consciousness and Clare's memories of the original, which is what was described in chapter 92, then i really don't see why someone else couldn't do the same thing. Perhaps created from a combination of Clare and Priscilla's memories, and whatever part of Teresa they put in Clare.
Conclusion
I think the 3rd Entity is a fragment of Teresa, which will eventually cause Priscilla to remember who she was and how much she hates Yoma. Then she will allow herself to be destroyed or uses her power as a parting gift to cause Teresa and Clare to be reborn. The legend of the twin goddesses given from. A new kind of Claymore and Rubel's worst nightmare.