Can think of a few who were kicked out of bands early doors to then form their own a la Dave Mustaine but really struggling to think of an established solo artist who did it. Bowie/Tin Machine maybe?
Bowie wanted to rescue his reputation after 1987's
Never Let Me Down and the Glass Spider tour, and this band did it.
I have to reference these quotes off of wiki as I was trying to remember how Tin Machine came together. First is from Bowie:
"I'd never wanted to be in a band until we got together. And as we were getting together, it wasn't really occurring to me that this is what I wanted to do. It took a week or so of actually being in the studio and working, and then I think we fully realized the potential, musically, for what we were doing and wanted to stick with it. I was quite happy to go off and make a solo album. I was quite excited about a couple of things I was doing, which I brought into the band and which were irrevocably changed. But that's the nature of the band."
"Their attitude was kind of, 'He's David Bowie, we're the Sales brothers, who the fuck are you?'" —Reeves Gabrels, on how the group bonded when they first came together.
Great stuff! ;-)
I'll put up established solo artist Sammy Hagar who joined established band Van Halen to still make it work. I'll take
5150 over anything David Lee Roth was putting out in his fullest self-obsessed Just-A-Gigolo timeframe.
James Gang, Barnstorm, and 3 album soloist Joe Walsh did fine in the Eagles as well, though I won't take some of you too far down that path. You can check out any time you like...
And there are plenty of other examples of bands who didn't make it work with their replacement band members.