It depends on the governing body. Florida does (Few disbarred lawyers ever seek readmission):
Retired Third District Court of Appeal Judge Alan Schwartz, chair of the Florida Board of Bar Examiners Character and Fitness Commission, said lawyers suspended for longer than three years would have to go through all the hoops that disbarred lawyers now face when they want to return to the practice of law.
However, this article states that Ohio does not allow reinstatement at all (Disbarred lawyers who seek reinstatement have a rough road to redemption):
Jonathan Coughlan: “In Ohio, there’s no such thing as reinstatement after disbarment—which includes being disbarred, resigning with discipline pending, or asking to retire and having that request accepted. Zero. Period. Do you know the definition of disbarment? It means you’re gone. It doesn’t allow you to come back. I tell my colleagues all the time: ‘If you want to allow the possibility of return, fine. But don’t call it disbarment.’”