Amy Coney Barrett has served on the United States Court of Appeals for the Seventh Circuit since 2017. Multiple outlets have reported that Trump will name her to replace the late Justice Ruth Bader Ginsburg. C-SPAN The GOP-led Senate will reportedly begin confirmation hearings on President Donald Trump's pick to replace the late Supreme Court Justice Ruth Bader Ginsburg on October 12, according to reports from The Hill and Politico on Saturday.