Taylor Swift, the biggest free agent in music, signed a long-term deal with the world’s biggest record company, Vivendi SA’s Universal Music Group, in the process using her clout to try to score some points for other artists signed to the same label.

Ms. Swift’s new deal came with a stipulation: Proceeds from any sale of Universal’s stockholdings in Spotify Technology SA are to be distributed to the label’s artists at a better rate than paid out previously by the other two majors.