Short version: some states will let you reapply after some number of years, and you have the opportunity to convince the court or the licensing agency that you have changed and whatever caused you to misbehave before is not an issue anymore (which is sometimes successfully argued in cases where for example alcohol/drugs or untreated mental illness were the root cause). Other states are effectively “death penalty” states: once disbarred, you are forever out and there is no possibility of or procedure for reinstatement.
In my state, it is at least theoretically possible to get reinstated. The person seeking reinstatement must file a petition with the Supreme Court, which will then solicit comments from members of the bar either in support or in opposition, and hold a hearing to consider those comments along with evidence of rehabilitation.