Before I begin with the answer to this question, let's see if we can come to some agreement on exactly what constitutes a Soul. There are countless definitions of "Soul", The soul is often described as the spiritual part of humans, a distinct entity, existing separate from the body and able to survive a physical death. There are some societies that believe a soul is something apart from yourself that is somewhere up there in the sky and there are some that believe that the soul is something that can be found somewhere within the physical body, and that in some grand gesture, upon death, we kneel before God and return the soul to Him.
For purposes of this discussion we will consider the soul as an almost unbelievably, sophisticated, indestructible energy essence personality. The soul is not some wispy fragment, cloud like existence, but to the contrary, the soul is the most potent, deliberately purposeful and self directed energy manifestation in the universe. The soul gives psychic birth to personalities and forms an undividable affiliation with that personality during its journey into physical life in a variety of realities. During the time that the personality is focused in a life on the physical plane, a portion of the soul is inexplicably intertwined within and a part of the personality. It would not be untrue to say that while you inhabit a physical body, you are the soul fleshed out in cells and molecules so that it can manipulate within the precise coordinates of your time and space. The soul thorough the auspices of the inner self creates the physical body, the seat of the ego self.
Any particular personality (identity) once formed can never be terminated, negated or diminished in any way. Once formed the identity is eternal. I want to make sure here that I make clear what I am saying; the Nancy, Robert, Charlene or Michael personality that you identify with now, will always be part of your eternal identity. Your memory will always include memory of those past personalities, their experiences, their loves, their failures and their triumphs, and if you have a habit of scratching your nose now, you may quite likely exhibit that habit in a future life. You will in a way always be the same you but you will be more. Your personality (the whole personality), is of course much more than just the ego self that you know, and it evolves whether it is in our system of reality and when it is outside of it. There are countless systems, planes, fields and dimensions of reality, some achieving three dimensional, physical characteristics like yours and some not physical at all. Physical reality such as yours is not the norm but it is unique in the way it has developed. There are none others quite like it in the universe as we know it although there are others very similar.
All systems of reality have their own unique characteristics and parameters for existence, none exactly like any other, but in all cases these parameters are created by the inhabitants of the system in which they exist. That means that each of you along with your contemporaries of your time had and have a hand in creating your own version of time, space, gravity and so forth. Reincarnation is one of the basic characteristics of all life on your physical plane. It is within this scope of reincarnation that you must consider the physical existence of "Old Souls". In light of that, all souls are old souls. A soul is an unbelievable advanced energy essence personality and in that respect, a soul has been around a very, very long time, so all souls would have to be considered old souls. In those terms, the physical personalities that it gives birth to can be either old or new. The soul honors that intimate connection with all of its personalities regardless of their state of evolution.
The soul has a thirst for experience so it seeks to objectify itself in a variety of different dimensions of actuality, creating the most appropriate forms suited for that particular system. The whole self, then creates the physical body through processes that we have discussed before and will again, but it should be understood that the physical image is created from the inside out through the abilities of the inner self. The whole self being the totality of the outer self (ego), connected to the inner self by the subconscious, these working together form the image of the physical body. Not one small heart, one eyelash or one tiny fingernail could be formed as parts of the fetus were it not for this complex inner process. A soul is made up of whole selves. Whole selves are made up of various aspects of the personality, (the ego, outer self and inner self) connected by the non physical mind and subconscious.
Once that minimal requirement is met, there are other options. The personality, if it is especially adept at the physical manipulation of matter and enjoys earthly life it may choose to reincarnate again even after the requirements have been met in order to experience different races, different physical impediments and deprivations and successes. It may not make sense to you at this point why someone would want to experience hardships, but you must understand that your motivations are not the motivations of your Soul. You are here to learn that you create your reality and what you create is not always perfect, so you will do it again. What you don't learn in one lifetime will be revisited in another and there is no rush as you have as many lives as you need. Often the most profound lessons are learned through personal misfortune. This series of lives must eventually end, lessons being learned, and the personality must make choices for future experience in other systems. Our Earth system is a beginning system and we must progress through it by the process of reincarnation and evolution before making future decisions. Some who are very evolved, having experienced many lifetimes, more so than their contemporaries, may choose to return to earth reality in future lives as teachers, taking on roles to inspire and show the way, so to speak. Of course, some very well known historic personalities will surely come to mind.
After your final incarnation in this reality, you will make choices for future development in any one of a myriad of systems that fit your own personal needs. You will not revisit Earth again, although you may retain fond memories of your experiences and lifetimes here. After you evolve beyond Earth reality, you will realize just how primitive it was. Those considered Old souls could certainly be old inasmuch as they would have seen many lifetimes here and are nearing the point of their departure from this plane. They ascend to greater things, meaning new and far more developed systems of reality of their choice. No one thing forces this decision; it is entirely up to the personality and its personal goals. At the same time, there are "New" consciousness always entering the system for the first time and they will be obvious to the more evolved.
By the way, ascension has nothing to do with so called "Heaven" and since there is no actual reality such as up or down, all being a matter of perception, it really does not make any sense at all to pray to God looking up. Ascension then does have something to do with evolutionary progress, in becoming more, but not better. There can be no better or best and consciousness cannot be qualified in that way because it is all from the same source. So, in answer to your question, our world is composed of both old and new identities, some having evolved to the point they are ready to leave our plane and some just arriving and beginning the evolutionary cycle but the soul stuff inherent and underlying each is very old indeed while the individual personalities inhabiting the physical forms may be youngsters. You will know them by their works.