I acknowledge this graphic from the Net.
This entity in this body passes through childhood to youth to old age
Then onto another body, which dos not disquiet the wise
The word ‘entity’ in the translation is my creation. In the verse in Sanskrit, Krishna uses no word to describe this movement from childhood to youth to old age and then at death to another body. Shankara uses the word Self in his commentary. Following the Upanishads, I would use the word That or more simply energy.
You can use any word you wish to describe the imperishable within that perishable body mind: Self, That or energy. It is the body mind that perishes at the end of a life time. It takes its own time, sometimes, sometimes not. Krishna here says with reference to Arjuna that the mind body passes through these stages of childhood, youth and old age. We can add more as Shakespeare did, with the seven stages in life. All that is created, those which are animate, grow. They grow in body, mind , skills and in several other aspects. With this growth ambitions grow.
We see many who after producing children, would like to see those children married. When their children marry, they would like to see them produce children. Then, they would like to see those grand children marry and produce. This desire is the survival instinct dominant in all of us. The question is, how long do we think this cycle can go on?
We know that some stage every body that is born and that grows, also dies. The mind body leaves with the last breath. Brain waves stop. Heart stops. The body left alone rots. Simply put, the mind body has reached its predetermined end and leaves. Something remains though! What is that something?
Krishna moves into that inquiry in the following verses.
Here he says: ‘That’ moves on to another body. According to Quantum Physics, matter and energy are convertible as Einstein postulated. Matter just does not perish. It becomes energy. So it is with our body mind. It becomes energy. That energy becomes matter again in another mind body.
Does this verse of Krishna prove reincarnation? I do not think so. I believe that when our mind body converts to energy at death, we become one with the universal energy. A part of that universal energy, a holographic part, becomes the driving energy of another mind body. Is it possible to identify where in that unlimited universal energy our tiny fractional energy is stored and track it down to another mind body?
In other verses in the Gita, Krishna does address this issue. Even those do not confirm reincarnation of one departing energy returning in entirety as another embodied entity.
For now, use this verse to console yourself and others that death is not the end of life, it is merely a gateway to another life, perhaps more fulfilling.