In law, to hold another trial for a case is to retry it. It's not legal in the U.S. to retry a defendant for a crime after she's been found innocent.
A judge might decide to retry a case if the jury can't come to a unanimous decision, or if a jury member is found to be biased. And when the defendant in a case is found guilty, they can appeal the decision in the hopes that the court will retry it, sometimes using a new attorney or new evidence. You probably won't use this verb to literally mean "try again" — you're more likely to say reattempt.