A high-profile holiday concert is getting a remix as ravers replace Phish-heads at one of the world’s biggest New Year’s Eve parties.

For the last four years, Phish has taken over Madison Square Garden to close out the year with a series of shows. Those stints—three or four sold-out nights in a row—climaxed Dec. 31 with a blowout production, and helped cement Phish’s standing as a singular force in live music.

This...