AMMAN—A former Jordanian royal court chief and a low-ranking member of the royal family pleaded not guilty on Monday to charges of agitating to destabilize the monarchy, one of their lawyers said. Prosecutors had referred to a military court the case of Bassem Awadallah, an ex-royal court chief and finance minister who played a big role in the drive to liberalize Jordan’s economy, and Sherif Hassan Zaid, a distant relative of King Abdullah. During the first session of the trial on Monday, both pleaded not guilty, according to Mohamed Afif, Awadallah’s lawyer. “Awadallah said he was not guilty and I have no ties to this case,” Afif said. Human rights activists have denounced the trial of civilians in the state security court, a special court they say is not independent of the judiciary and lacks standards of a fair trial. The pair were arrested in early April when former heir …