The Disincarnate Counterpart is one which decided to transition during the course of this lifetime. They pass away and move into the higher states of consciousness or into New Earth before the other one. This can be incredibly painful to have such a profound love and then go through the grief of loss in losing their physical presence. This from my understanding is designed to help the other Ascension process to grow their gifts and abilities to the non physical world and of course they will meet again after this lifetime or in New Earth. The Counterpart who has passed over will serve as a spirit guide who will help love and support the other from the non physical.
Other types of Disincarnate Counterparts can be where one has decided to incarnate on to the Earth at this time and the other has decided to stay back in the Higher Dimensional realms to be the guide from the other side.
Finally this may also be applied to the Galactic Counterpart as well, where some may be incarnated here on Earth while their counterpart does not take a physical form and instead stays on the Spacecraft in their Galactic embodiment. This way they will still have encounters with each other in the Astral or while on craft. They are able to serve out their mission together as one will work from the Earth and the other in outer space for a larger galactic mission.