I can only think of two right off the top of my head:
-Van Halen. Wildly successful with David Lee Roth as the lead singer. Replaced with Sammy Hagar, and the band continued to be successful.
-Genesis. Peter Gabriel was the lead singer for the band, from its onset in 1967 until 1976. The band continued to enjoy popularity after he left and Phil Collins took over lead vocals.
I know other bands have tried it (Motley Crue with John Corabi instead of Vince Neil for one).
I’m not looking for bands that didn’t become popular/established until they replaced their original singer. Just bands that were already well-known before the replacing happened.
Fleetwood Mac were very successful in the U.K. with Peter Green and Jeremy Spencer as lead vocalists, and, later, successful worldwide with Christine McVie, Stevie Nicks and Lindsay Buckingham. Of course, they also changed their whole sound. (There were others singing lead in between, such as Danny Kirwan and Bob Welch, but the band was not so successful in that period.)
Black Flag had four vocalists: Keith Morris, Ron Reyes, Dez Cadena, and Henry Rollins. The band was pretty popular in punk circles during Dez’s stint, and remained popular (and is probably best remembered, much to the chagrin of some purists) during Henry’s time at the microphone.
Sort of - there is no lead singer, they’re a vocal group where each member is, in theory, on the same level as the others, and while they haven’t had number ones with every lineup they have managed to stay successful.