The last time Coldplay released an album, 2014’s subdued “Ghost Stories,” the British rock band skipped the blockbuster concert tour that would normally come next. One reason: Singer Chris Martin had recently separated from his wife of 10 years, Gwyneth Paltrow, and wasn’t eager for the spotlight. Instead, Coldplay immediately started work on a follow-up album.

Now, Mr. Martin and his bandmates—Jonny Buckland (guitar), Guy Berryman (bass) and Will Champion (drums)—are eager to open the throttle again. The group’s seventh...