In plain words
There one regains the connection with the buddhi cultivated in a former body, and on that basis strives still more toward perfection, joy of the Kurus.
Word for word
There [he] gains that union with buddhi of the former body, and from that strives more for perfection, O joy of the Kurus.
The commentators
Bhagavadgītābhāṣyam
यस्मात् —
तत्र योगिनां कुले तं बुद्धिसंयोगं बुद्ध्या संयोगं बुद्धिसंयोगं लभते पौर्वदेहिकं पूर्वस्मिन् देहे भवं पौर्वदेहिकम् । यतते च प्रयत्नं च करोति ततः तस्मात् पूर्वकृतात् संस्कारात् भूयः बहुतरं संसिद्धौ संसिद्धिनिमित्तं हे कुरुनन्दन ॥ ४३ ॥
In plain words
And here's why —
There, born into a family of yogīs, he regains that connection with the intellect he had built up in his former body. And from that impression carried forward, he strives—makes an even greater effort this time—toward perfection, joy of the Kurus.
Close to the Sanskrit
Because —
There, in the family of yogīs, he obtains that union with the intellect—i.e. union with the intellect—belonging to the former body, i.e. existing in the former body; and he strives, i.e. makes effort, from that, i.e. from that previously acquired impression, further, greater, toward perfection, for the sake of perfection, O joy of the Kurus.