If the defendant did not waive the right to appeal in a plea agreement, the defense may appeal both the conviction and the sentence imposed. The public defender will continue to represent the defendant, for free, during the appeal. There is a very short period during which the defense must state its intention to appeal (“notice” an appeal), so the subject should be discussed immediately after sentencing. See Fed. R. App. Pro. 4(b).
If the defendant does not win the appeal in the Ninth Circuit, he or she can file a petition for writ of certiorari with the Supreme Court of the United States. The public defender will continue to represent the defendant during the petition for certiorari and Supreme Court argument, if the writ is granted.