Sri Aurobindo uses the term Gnostic Being to designate the state of the individual who has realised the Supramental State. This is described in Book 2 Chapter 27 of The Life Divine. There is a very good online summary by Roy Posner - Chapter 27 - The Gnostic Being Chapter 28 - The Divine Life
This will be a supramental state of divinised post-humanity, which (as described in the final chapters of ) will emerge as a spirit-oriented future existence.
In this highest form of social or collective life, the domination of the ordinary mind — of surface preoccupation, of partial knowledge, as well as the lower physical and vital life is replaced with a mind and life dominated by the spirit.
A parallel but also somewhat different description is found in the Agenda. In the Supermental State, if the Agenda is anything to go by, we no longer exist as we were before. We no longer are mental and emotional beings, our bodies themselves embody God. The physical body itself becomes God, i.e. it allows God (the Supreme, Supermind, whatever) to work through it. The body itself becomes the instrument of the Supreme, free of any resistance, any dullness, any rigidity, and atavistic habits, and this is the new, perfect, deathless, divine life.
What might life be like on the other side of the Spiritual Singularity? We can only speculate, and poorly at that. Actions would still be done, but in a perfect way, as expressions of the Divine Light and the Harmony of the Greater Whole. But although we would exist in oneness, we would still retain our individuality, and act freely. Only it is a different sort of individuality to what we have now. It would be an individuality of the Divine Soul, not of the Ego (which would no longer exist). And in the sense that we would be conscious of our divinity, every being would be an avatar so to speak. And (if the Agenda is any guide) our physically existence would be totally different to the physical existence we have now.
Sri Aurobindo describes the divinised or gnostic being is described as living a spiritual existence in an integral way; integral in his own being, and integral and one with the world around him. He has integrated and elevated the physical, vital/emotional, and mental planes of his existence to its greatest heights and fulfillment by finding the spirit within himself and applying and elevating these planes of life with the spiritual. He also discovers that the spirit is everywhere in the world and in every other person, eliminating the separation between himself and life and himself and others around him. In other words he is whole and integrated individually and universally.
"To be in the being of all and to include all in one's being, to be conscious of the consciousness of all, to be integrated in force with the universal force, to carry all action and experience in oneself and feel it as one's own action and experience, to feel all selves as one's own self, to feel all delight of being as one's own delight of being is a necessary condition of the integral divine living."
In addition to integrating the planes and sublevels of one's being (individualization), and becoming one with others and the world around is (universalization), the individuals who will be the harbingers of this divine life will also be united with the transcendent Divine. These individuals will have found the transcendent spirit within, the spiritual force, God, the Divine in the cosmos, and feel, know, act with complete reference to its divine force, power, knowledge, and bliss.
In this context a number of individuals, integrated individually, universally, and transcendently, can work together, near or apart, aware or unaware of one another, to create a new common life, superior to the present individual and common existence. A critical mass of such "gnostic individuals" could create the foundation of a new social life and order; a divine life on earth. The purpose of this divine life would be a greater unity, mutuality, and harmony.
"...a greater identity of being and consciousness between individual and individual unified in their spiritual substance, feeling themselves to be self and self of one self-existence, acting in a greater unitarian force of knowledge, a greater power of being. There must be an inner and direct mutual knowledge, based upon a consciousness of oneness and identity, a consciousness of each other's being, thought, feeling, inner and outer movements...."
In this state the current vital and mental constructions of life would be replaced by gnostic individuals who live beyond the vicissitudes of human thought and the push and pull of the forces of Nature. Humanity in the current age does not have the depth of inner knowledge to understand the infinite forces that are involved in the emerging world. His limiting mind-sense and the limiting mind-sense of the collective hasn't the integral vision and knowledge and force of action to deal with the evolving society. We have created a civilization which has become too big for our limited mental capacities and understanding and our limiting ego, which narrows the truth to our own needs and desires. The current unfolding and limited blossoming of life on earth is bound by the limiting vital animal and passion nature, and the narrow opening to the full truth which is the human mind.
A life of unity, mutuality, and harmony alone, emerging from individuals who are in integral relationship with themselves, others, and the transcendent spirit, can deal with the overwhelming needs of the collective life. The gnostic beings help establish this integral, unifying gnostic consciousness on earth, it would provide a far greater power and knowledge than mental man has for understanding and acting on the needs of the emerging collective. The one rule of this divine life would be the self expression of the spirit, of the divine, in all aspects of life.
"..an existence without the reactions of success and frustration, vital joy and grief, peril and passion, pleasure and pain, the vicissitudes and uncertainties if fate and struggle and battle and endeavor, a joy of novelty and surprise and creation projecting itself into the unknown... The gnostic manifestation of life would be more full and fruitful and its interest more vivid than the creative interest of the Ignorance; it would be a greater and happier constant miracle."