Many electrons in an atom are entangled with each other. I don't think it's possible to specify every combination that could occur. Possible spin entanglement with the nucleus too.
In a pair in a specific orbital, where one has spin up and the other is spin down - and indistinguishable, I would expect entanglement. However, I am not sure the entanglement would be monogamous if other orbitals have indistinguishable electrons.