Prepare for a storm of publicity, he told one of the start-ups that he had helped found. There would be questions about his political affiliations and loyalties, he said. There would be questions about the survivability of the start-up, a health insurance company named Oscar Health. The world was about to change, he said.

The venture capitalist was Joshua Kushner, whose older brother is Jared Kushner — the husband of Ivanka Trump and one of President-elect Donald J. Trump's closest confidants. And that meeting at Oscar Health was just the beginning of a new and unsettling chapter for the younger Mr. Kushner.

At 31, Joshua Kushner has built his technology investment firm — Thrive Capital, which has financed the photo-sharing app Instagram and the e-commerce company Jet.com, among others — largely behind the scenes, keeping his head down while pursuing deals. But with his older brother's rising profile and growing role in the incoming administration, Mr. Kushner is now getting caught up in the scrutiny. Two of his worlds are colliding.