It’s always kind of weird to me to see a seriously established performer join a famous band, and then the band will add their solo work to their set list.
I can think of three examples.
Joe Walsh in The Eagles. Now this was very early for them, and admittedly Im not familiar with Walsh’s pre-Eagles work.
Larry Gowan in Styx. This was actually a while back. But past their heyday. I know they play at least ‘Criminal Mind’ and Larry is a more then suitable replacement for Dennis DeYoung.
Neil Finn in Fleetwood Mac. This is the weirdest one. Seeing Fleetwood Mac playing Neil Finns work. Whether its Crowded House or Split Enz. I don’t anticipate Fleetwood Mac to be around very much longer
What others? I don’t mean Supergroups or just any old replacement unless they were somewhat famous.
Edit: I see Vince Gill joined The Eagles in 2017. I didn’t know that before today.
Joe Strummer fronting the Pogues after they tossed out Shane MacGowan has gotta be up there. That ensemble would drop “London Calling” into the live set.
Ronnie James Dio was already well-established from his time in Elf and Rainbow, and his early solo career, before he took Ozzy’s place in Black Sabbath.
And when he in turn left the band, it was Ian Gillan of Deep Purple who took his place on the following album and tour, on which Sabbath added “Smoke on the Water” to their setlist.
Dave Navarro of Jane’s Addiction was a member of Red Hot Chili Peppers from 1993 and 1998, replacing John Frusciante. He recorded One Hot Minute with them and went on tour, but I don’t know if they played any JA songs.
They did, indeed, but the OP was specifically asking about new members whose previous songs got incorporated into their new band’s setlist (though that part of their question is in their post, not in the thread title).
I don’t know if Fleetwood Mac regularly (if ever) played any of the songs that Lindsey and Stevie had from their earlier work.
Jon Anderson (Yes’s longtime lead singer) did several collaboration albums with Vangelis, but Vangelis was never an actual member of Yes.
And, while Yes has, indeed, had a ton of members, for the most part, their membership hasn’t been a matter of a big-name artist who was in another band (or a solo act) joining them.
In the early 1980s, when singer/guitarist Trevor Rabin replaced Steve Howe in their lineup, he brought with him a number of songs he’d been working on, several of which made it onto the 90125 album (most notably “Owner of a Lonely Heart”), but Rabin wasn’t particularly well-known outside of his native South Africa at that point, and those songs weren’t ones that Rabin had already recorded and had any sort of success with.
Vinnie Paul played a single Pantera song with Avenged Sevenfold after their original drummer died. He didn’t actually join the band, and the band already covered the song (Mouth for War) in their live setlist sometimes.
Mike Portnoy’s various post-Dream Theater projects have usually covered Dream Theater songs.
I first thought of Van Halen’s other other singer, Gary Cherone, but I’m not sure if Van Halen played any of Gary or Extreme’s music on tour. Gary’s single tour with Van Halen was noteworthy mostly for reviving older Van Halen songs that Sammy Hagar apparently didn’t want to perform.