In early December, Island Records co-­chairmen/co-CEOs Justin Eshak and Imran Majid traveled to the north coast of Jamaica to visit the 87-year-old founder of the label they now run, Chris Blackwell.

Morgan Wallen and Sabrina Carpenter (the latter whose label Island Records is included in REPUBLIC’s market share along with Cash Money, Wallen’s labels Mercury and Big Loud and indie ...