John Hiatt. Before solo he was in a group named White Duck. Two albums on Uni Records, I believe---I have the first. You don’t need it. ;-)
NIck Lowe was in The Brinsley Schwarz Band, Dave Edmunds in Love Sculpture. Both more successful and imo far better as solo artists.
Van Morrison was of course in Them, who were a great band. But he’s sold a lot more records on his own.
Moon Martin (writer of "Bad Case Of Loving You" and "Cadillac Walk") was in Southwind. Two albums on Blue Thumb Records, both of which I own.
Boz Scaggs was a member of The Steve Miller Band (first two albums).
Dan Hicks was the drummer in The Charlatans. When he switched to guitar, vocals, and songwriting he became one of my favorite artists of the 70’s and beyond.
Though both Neil Young and Steven Stills were pretty darn successful (and great) in Buffalo Springfield, they were even more so when they left that fantastic group.
Jimmie Dale Gilmore, Joe Ely, and Butch Hancock all rose to greater heights on their own than they had in their trio named The Flatlanders.
Maria Muldaur ("Midnight At The Oasis") got her start as a member of The Jim Kweskin Jug Band. I guess Maria provided the jugs. ;-0