Krishna speaks6.43

तत्र तं बुद्धिसंयोगं लभते पौर्वदेहिकम्।यतते च ततो भूयः संसिद्धौ कुरुनन्दन॥

tatra taṃ buddhi-sanyogaṃ labhate paurva-dehikamyatate ca tato bhūyaḥ sansiddhau kuru-nandana

Word by word
tatratheretamthatbuddhi-sanyogamreawaken their wisdomlabhateobtainspaurva-dehikamfrom the previous livesyatatestrivescaandtataḥthereafterbhūyaḥagainsansiddhaufor perfectionkuru-nandanaArjun, descendant of the Kurus

The verse says

There he regains the connection of understanding that belonged to his former body, and from there he strives further toward completion.

In plain words

The point of the whole passage, in one line.

Paurva-dehikam — belonging to the earlier body.

Whatever was built is not lost. It is picked up.

Where you've felt this · in growing older

You pick up the instrument again after eighteen years and your hands know more than you do. You are not starting over. You are resuming, and the difference is enormous.

Going deeper

Whatever a reader thinks about rebirth, the structure of this claim is worth having.

What is described is not a reward waiting somewhere. It is a continuity: the understanding built before is still there, and work resumes from where it stopped rather than from nothing.

Bhūyaḥ — again, further. He strives more, from a position he did not have to rebuild.

And the ordinary version of this is testable within a single life. Skills lie dormant for decades and come back faster than they were learned. Something that was worked at does not entirely leave, even when the person has stopped and forgotten and would tell you they lost it.

Which is the reassurance Arjuna actually asked for at 6.37. Not that he will finish. That the part he did will still be there when he picks it up.