Last year, James Corden departed from The Late Late Show, which meant the end of a segment that had become an institution in the music landscape: “Carpool Karaoke.” Well, surprise: It’s back!

Liam died aged 31 on October 16 after falling from the third-floor balcony of a hotel in the Argentine capital Buenos Aires. His close pal actor and presenter James, 46, was among many stars who came ...