SAN FRANCISCO — When Twitter was looking for a corporate legal director a few years ago, it asked Ted Wang, the company's first outside counsel, to review a candidate named Vijaya Gadde.

At the time, Gadde was a senior director and associate general counsel at Juniper Networks, coming off a decade at Wilson Sonsini Goodrich & Rosati. Right away, Wang said, it was clear that she had deep subject matter experience in securities, corporate governance and M&A. She seemed bright, upbeat and good to be around — someone with whom Wang, as outside counsel at Fenwick & West, might like working.